{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":61157,"title":"Scaling vertically parabola by evaluating its area over an interval","description":"Let p be a quadratic polynomial, with its axis of symmetry being the y-axis. Considering the vertical shift of its vertex to the origin, find the positive constant, k, that scales the shifted parabola such that its area over the interval [-a; a] (a\u003e0) will be equal to the area under the original parabola (see figure below).\r\ninput: (p, a)\r\noutput: k\r\n\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 447.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 223.9px; transform-origin: 408px 223.9px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be a quadratic polynomial, with its axis of symmetry being the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis. Considering the vertical shift of its vertex to the origin, find the positive constant, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, that scales the shifted parabola such that its area over the interval \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[-a; a] (a\u0026gt;0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be equal to the area under the original parabola (see figure below).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(p, a)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 255.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 127.9px; text-align: left; transform-origin: 384px 127.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"326\" height=\"250\" style=\"vertical-align: baseline;width: 326px;height: 250px\" src=\"data:image/png;base64,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\" alt=\"Scale parabola\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function k = scale_parabola(p, a)\r\n  k = x;\r\nend","test_suite":"%%\r\np = [1 0 1];\r\na = 2;\r\nk_correct = 7/4;\r\nassert(isapprox(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [1 0 -1];\r\na = 2;\r\nk_correct = 0.25;\r\nassert(isapprox(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [5 0 0];\r\na = 0.5;\r\nk_correct = 1;\r\nassert(isequal(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\nfiletext = fileread('scale_parabola.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [-3 0 1];\r\na = 1;\r\nk_correct = 0;\r\nassert(isequal(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [-3 0 2];\r\na = 1;\r\nk_correct = -1;\r\nassert(isequal(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [-3 0 2];\r\na = 3;\r\nk_correct = 7/9;\r\nassert(isapprox(scale_parabola(p,a),k_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-16T14:57:57.000Z","deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2026-01-16T14:57:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-10T14:36:03.000Z","updated_at":"2026-03-29T13:27:42.000Z","published_at":"2026-01-15T14:52:59.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be a quadratic polynomial, with its axis of symmetry being the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis. Considering the vertical shift of its vertex to the origin, find the positive constant, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, that scales the shifted parabola such that its area over the interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[-a; a] (a\u0026gt;0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be equal to the area under the original parabola (see figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(p, a)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"250\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"326\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Scale parabola\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60566,"title":"Given a Polyshape_01 (ps) Return its Perimeter, Area, and Centroid.","description":"Return the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\r\nReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\r\nReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 52.3333px; transform-origin: 407.5px 52.3333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.8333px; text-align: left; transform-origin: 384.5px 10.8333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21.6667px; text-align: left; transform-origin: 384.5px 21.6667px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.8333px; text-align: left; transform-origin: 384.5px 10.8333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"%%\r\nfunction [P, A, Cx, Cy] = PolyShape_01(ps)\r\n    % Return the perimeter (P) of a polyshape object, which is the sum\r\n    % of the lengths of its boundaries.\r\n    \r\n    % Return the total area (A) of a polyshape object, which is the sum\r\n    % of the areas of the solid regions that make up the polyshape.\r\n    \r\n    % Return the x-coordinate (Cx) and the y-coordinate (Cy) of the\r\n    % centroid of a polyshape. \r\n end","test_suite":"%% Test 1\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),1313))\r\n    assert(isequal(round(A,4),134508.0227))\r\n    assert(isequal(round(Cx,4),17))\r\n    assert(isequal(round(Cy,4),47))\r\n\r\n    \r\n%% Test 2\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),1313))\r\n    assert(isequal(round(A,4),134508.0227))\r\n    assert(isequal(round(Cx,4),254))\r\n    assert(isequal(round(Cy,4),-1676))\r\n\r\n    \r\n%% Test 3\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),177.255))\r\n    assert(isequal(round(A,4),2451.4087))\r\n    assert(isequal(round(Cx,4),34.29 ))\r\n    assert(isequal(round(Cy,4),-226.26))\r\n\r\n    \r\n%% Test 4\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),206.155))\r\n    assert(isequal(round(A,4),2385.7031))\r\n    assert(isequal(round(Cx,4),34.0501))\r\n    assert(isequal(round(Cy,4),-226.4324))\r\n\r\n    \r\n%% Test 5\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[20, -220],'SideLength', 1.7));\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),235.055))\r\n    assert(isequal(round(A,4),2319.9976))\r\n    assert(isequal(round(Cx,4),34.448))\r\n    assert(isequal(round(Cy,4),-226.6146))\r\n\r\n    \r\n%% Test 6\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[20, -220],'SideLength', 1.7));\r\n    ps = subtract(ps,polyshape([20 30.1 40.1 45.1 50 45.2 40.2 30.2 27.2],[-235 -239 -239 -237 -235 -239 -241 -240.5 -240]));\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),300.0489))\r\n    assert(isequal(round(A,4),2274.2476))\r\n    assert(isequal(round(Cx,4),34.4235))\r\n    assert(isequal(round(Cy,4),-226.367))\r\n    \r\n    \r\n    ","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":20795,"edited_by":20795,"edited_at":"2024-06-28T13:41:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-26T18:00:30.000Z","updated_at":"2026-03-18T15:16:22.000Z","published_at":"2024-06-26T18:18:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eReturn the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2447,"title":"Musical Note Interval 1 - Diatonic Scale","description":"Assuming a simple diatonic C scale, calculate the interval (integer) between two notes (provided as strings). By applying numbers to the notes of the scale (C,D,E,F,G,A,B,C = 1,2,3,4,5,6,7,8), intervals can be calculated. Because a unison is defined as one rather than zero, you add one to the numerical difference. The intervals are defined as:\r\n\r\nC - C: perfect unison, 1\r\n\r\nC - D: major second, 2\r\n\r\nC - E: major third, 3\r\n\r\nC - F: perfect fourth, 4\r\n\r\nC - G: perfect fifth, 5\r\n\r\nC - A: major sixth, 6\r\n\r\nC - B: major seventh, 7\r\n\r\nFor example, if the input is {'C','G'} the output will be a perfect fifth: 5-1+1=5. For input {'E','A'} the output will be a perfect fourth: 6-3+1=4.\r\n\r\nFor intervals that wrap around the scale, add seven to the resulting negative number to obtain the correct interval. For example, for {'A','C'} the output will be a major third: 1-6+1=-4, -4+7=3.","description_html":"\u003cp\u003eAssuming a simple diatonic C scale, calculate the interval (integer) between two notes (provided as strings). By applying numbers to the notes of the scale (C,D,E,F,G,A,B,C = 1,2,3,4,5,6,7,8), intervals can be calculated. Because a unison is defined as one rather than zero, you add one to the numerical difference. The intervals are defined as:\u003c/p\u003e\u003cp\u003eC - C: perfect unison, 1\u003c/p\u003e\u003cp\u003eC - D: major second, 2\u003c/p\u003e\u003cp\u003eC - E: major third, 3\u003c/p\u003e\u003cp\u003eC - F: perfect fourth, 4\u003c/p\u003e\u003cp\u003eC - G: perfect fifth, 5\u003c/p\u003e\u003cp\u003eC - A: major sixth, 6\u003c/p\u003e\u003cp\u003eC - B: major seventh, 7\u003c/p\u003e\u003cp\u003eFor example, if the input is {'C','G'} the output will be a perfect fifth: 5-1+1=5. For input {'E','A'} the output will be a perfect fourth: 6-3+1=4.\u003c/p\u003e\u003cp\u003eFor intervals that wrap around the scale, add seven to the resulting negative number to obtain the correct interval. For example, for {'A','C'} the output will be a major third: 1-6+1=-4, -4+7=3.\u003c/p\u003e","function_template":"function interval = note_interval(notes)\r\n interval = 0;\r\nend","test_suite":"%%\r\nnotes = {'C','G'};\r\ninterval = 5;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'C','E'};\r\ninterval = 3;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'G','C'};\r\ninterval = 4;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'C','B'};\r\ninterval = 7;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'C','C'};\r\ninterval = 1;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'E','A'};\r\ninterval = 4;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'D','C'};\r\ninterval = 7;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'D','E'};\r\ninterval = 2;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'A','C'};\r\ninterval = 3;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'C','A'};\r\ninterval = 6;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'C','E'};\r\ninterval = 3;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'E','C'};\r\ninterval = 6;\r\nassert(isequal(note_interval(notes),interval))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":42,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-07-18T15:06:07.000Z","updated_at":"2026-03-17T11:56:46.000Z","published_at":"2014-07-18T15:06:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssuming a simple diatonic C scale, calculate the interval (integer) between two notes (provided as strings). By applying numbers to the notes of the scale (C,D,E,F,G,A,B,C = 1,2,3,4,5,6,7,8), intervals can be calculated. Because a unison is defined as one rather than zero, you add one to the numerical difference. The intervals are defined as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eC - C: perfect unison, 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eC - D: major second, 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eC - E: major third, 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eC - F: perfect fourth, 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eC - G: perfect fifth, 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eC - A: major sixth, 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eC - B: major seventh, 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if the input is {'C','G'} the output will be a perfect fifth: 5-1+1=5. For input {'E','A'} the output will be a perfect fourth: 6-3+1=4.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor intervals that wrap around the scale, add seven to the resulting negative number to obtain the correct interval. For example, for {'A','C'} the output will be a major third: 1-6+1=-4, -4+7=3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61151,"title":"Scaling vertically functions","description":"Given a real function by the 1×n array, x, of inputs and the 1×n array, y, of outputs, consider shifting vertically its graph by the scale factor k (see figure below). Return\r\ny_scaled, which is the 1×n vector that stands for the outputs of the scaled function;\r\ns = 'strech' or 'compress', if the graph will be away from or towards the x-axis, respectively, becoming narrower or wider relative to the original function's graph. Return s = '', if there is no change in size;\r\nr = 'flip' or 'flat' if the graph will be reflected over the x-axis or collapses the entire graph onto the x-axis, respectively. Return r = '', if the orientation is preserved.\r\ninput: (x, y, k)\r\noutput: [y_scaled, s, r]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 489.987px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 244.988px; transform-origin: 408px 244.994px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a real function by the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of inputs and the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eof outputs, consider shifting vertically its graph by the scale factor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see figure below). Return\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.188px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 51.0875px; transform-origin: 391px 51.0938px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey_scaled\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e vector that stands for the outputs of the scaled function;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 'strech' or 'compress', if the graph will be away from or towards the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis, respectively, becoming narrower or wider relative to the original function's graph. Return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = '', if there is no change in size;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 'flip' or 'flat' if the graph will be reflected over the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis or collapses the entire graph onto the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis, respectively. Return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = '', if the orientation is preserved.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(x, y, k)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[y_scaled, s, r]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 255.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 127.9px; text-align: left; transform-origin: 384px 127.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"369\" height=\"250\" style=\"vertical-align: baseline;width: 369px;height: 250px\" src=\"data:image/png;base64,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\" alt=\"Scaling function's graph\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [y_scaled, s, r] = scaling(x,y,k)\r\n  y_scaled = x;\r\n  s = x;\r\n  r = x;\r\nend","test_suite":"%% \r\nx  = [0 1 2 5 10 15 20 25];\r\ny = [4 4.6 4.4 3.4 3.1 1.8 1.4 2];\r\nk = 2.62; \r\ny_correct = [10.48  12.052  11.528  8.908  8.122  4.716  3.668  5.24];\r\ns_correct = 'stretch';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -pi/2:pi/12:pi/2;\r\ny = sin(x).*cos(x);\r\nk = 2;\r\ny_correct = sin(2*x);\r\ns_correct = 'stretch';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -pi/2:pi/12:pi/2;\r\ny = 1 - cos(2*x);\r\nk = 0.5;\r\ny_correct = (sin(x)).^2;\r\ns_correct = 'compress';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -pi:pi/6:pi;\r\ny = (sin(x)).^2;\r\nk = - 1;\r\ny_correct = (cos(x)).^2 -1;\r\ns_correct = '';\r\nr_correct = 'flip';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -5:5;\r\ny = atan(x);\r\nk = 0;\r\ny_correct = 0.*x;\r\ns_correct = 'compress';\r\nr_correct = 'flat';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nfiletext = fileread('scaling.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = -2:0.5:2;\r\ny = polyval([1/3 0 -1 0], x);\r\nk = 3;\r\ny_correct = [-2 9/8 2 11/8 0 -11/8 -2 -9/8 2];\r\ns_correct = 'stretch';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(isequal(s, s_correct))\r\nassert(isequal(r, r_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-11T13:38:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-06T11:12:26.000Z","updated_at":"2026-03-28T12:45:32.000Z","published_at":"2026-01-11T13:38:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a real function by the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of inputs and the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eof outputs, consider shifting vertically its graph by the scale factor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see figure below). Return\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey_scaled\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e vector that stands for the outputs of the scaled function;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 'strech' or 'compress', if the graph will be away from or towards the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis, respectively, becoming narrower or wider relative to the original function's graph. Return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = '', if there is no change in size;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 'flip' or 'flat' if the graph will be reflected over the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis or collapses the entire graph onto the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis, respectively. Return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = '', if the orientation is preserved.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(x, y, k)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[y_scaled, s, r]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"250\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"369\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Scaling function's graph\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61164,"title":"Comparing to scale all terms versus one term of even-degree polynomial by the same scale factor","description":"Let p be an even-degree polynomial with positive leading coefficient. Consider the scale factor, k,  that vertically transforms the polynomial p by scaling (1) the entire function and (2) only the leading coefficient (see figure below). To compare both cases, (1) and (2), find\r\nV0, the m0×2 matrix that represents the vertex of the original polynomial p;\r\nV1, the m1×2 matrix that represents the scaled vertex for case 1:\r\nV2, the m2×2 matrix that represents the scaled vertex for case 2;\r\nwhere 1 \u003c= m0, m1, m2 \u003c n and n stands for the degree of polynomial (see Hint). Return the first column of each matrix sorted by increasing x-values (in ascending order), while the y-value of the vertex in the second column. \r\nHint. The vertex of an even-degree polynomial is not necessarily unique, i.e., the global extremum may be reached at m, multiple distinct, x-values.\r\ninput: (p, k)\r\noutput: [V0, V1, V2]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 611.112px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 305.55px; transform-origin: 469px 305.556px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 21px; text-align: left; transform-origin: 445px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be an even-degree polynomial with positive leading coefficient\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider the scale factor, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,  that vertically transforms the polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by scaling (1) the entire function and (2) only the leading coefficient (see figure below). To compare both cases, (1) and (2), find\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 452px 30.65px; transform-origin: 452px 30.6562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 424px 10.2125px; text-align: left; transform-origin: 424px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eV0,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix that represents the vertex of the original polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 424px 10.2125px; text-align: left; transform-origin: 424px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eV1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix that represents the scaled vertex for case 1:\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 424px 10.2125px; text-align: left; transform-origin: 424px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eV2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix that represents the scaled vertex for case 2;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 21px; text-align: left; transform-origin: 445px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1 \u0026lt;= m0, m1, m2 \u0026lt; n \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the degree of polynomial (see Hint). Return the first column of each matrix sorted by increasing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-values (in ascending order), while the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-value of the vertex in the second column. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 21px; text-align: left; transform-origin: 445px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint. The vertex of an even-degree polynomial is not necessarily unique, i.e., the global extremum may be reached at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, multiple distinct, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-values.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(p, k)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-style: italic; \"\u003e[V0, V1, V2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 315.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 157.9px; text-align: left; transform-origin: 445px 157.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"265\" height=\"310\" style=\"vertical-align: baseline;width: 265px;height: 310px\" src=\"data:image/png;base64,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\" alt=\"Comparing scales\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [V0, V1, V2] = vertices(p,k)\r\n  V0 = x;\r\n  V1 = x;\r\n  V2 = x;\r\nend","test_suite":"%%\r\np = [1 -4 -3];\r\nk = 5;\r\nV0_correct = [2 -7];\r\nV1_correct = [2 -35];\r\nV2_correct = [0.4 -3.8];\r\n[V0, V1, V2] = vertices(p,k);\r\nassert(isequal(V0,V0_correct))\r\nassert(isequal(V1,V1_correct))\r\nassert(isequal(V2,V2_correct))\r\n\r\n%%\r\np = [0.25 -1 -2 0 0];\r\nk = 4;\r\nV0_correct = [4 -32];\r\nV1_correct = [4 -128];\r\nV2_correct = [(3+sqrt(73))/8 -(827+73*sqrt(73))/2^9];\r\n[V0, V1, V2] = vertices(p,k);\r\nassert(isequal(V0,V0_correct))\r\nassert(isequal(V1,V1_correct))\r\ntolerance = 1e-13;\r\nassert(all(abs(V2 - V2_correct) \u003c tolerance))\r\n\r\n%%\r\np = [0.5 2.4 -3 -22 4.5 54 30.4];\r\nk = 5;\r\nV0_correct = [-1 -2];\r\nV1_correct = [-1 -10];\r\nV2_correct = [-0.901803848596367 -0.57405744023312];\r\n[V0, V1, V2] = vertices(p,k);\r\nassert(all(isapprox(V0,V0_correct), 'all'))\r\ntolerance = 1e-13;\r\nassert(all(abs(V1 - V1_correct) \u003c tolerance))\r\nassert(all(abs(V2 - V2_correct) \u003c tolerance))\r\n\r\n%%\r\nfiletext = fileread('vertices.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [3 0 0 0 1];\r\nk = 1/3;\r\nV0_correct = [0 1];\r\nV1_correct = [0 1/3];\r\nV2_correct = [0 1];\r\n[V0, V1, V2] = vertices(p,k);\r\nassert(isequal(V0,V0_correct))\r\nassert(all(isapprox(V1,V1_correct), 'all'))\r\nassert(isequal(V2,V2_correct))\r\n\r\n%%\r\np = [0.5 3 7.5 11 11 8 4];\r\nk = 10;\r\nV0_correct = [-2 0];\r\nV1_correct = [-2 0];\r\nV2_correct = [-0.590924701770178 1.75514977256519];\r\n[V0, V1, V2] = vertices(p,k);\r\ntolerance = 1e-13;\r\nassert(all(abs(V0 - V0_correct) \u003c tolerance))\r\nassert(all(abs(V1 - V1_correct) \u003c tolerance))\r\nassert(all(abs(V2 - V2_correct) \u003c tolerance))\r\n\r\n%%\r\np = [0.25 -2 1.5 10 0];\r\nk = 0.2;\r\nV0_correct = [-1 -6.25; 5 -6.25]; \r\nV1_correct = [-1 -1.25; 5 -1.25];\r\nV2_correct = [29.43264376174156 -11878.00773655344];\r\n[V0, V1, V2] = vertices(p,k);\r\nassert(all(isapprox(V0,V0_correct), 'all'))\r\nassert(all(isapprox(V0(1,:), V0_correct(1,:)), 'all'))\r\ntolerance1 = 1e-13;\r\nassert(all(abs(V1(2,:) - V1_correct(2,:)) \u003c tolerance1))\r\ntolerance = 1e-11;\r\nassert(all(abs(V2 - V2_correct) \u003c tolerance))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-04-02T17:08:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2026-04-02T17:08:16.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-14T14:02:53.000Z","updated_at":"2026-04-03T19:14:06.000Z","published_at":"2026-01-19T17:28:19.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be an even-degree polynomial with positive leading coefficient\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the scale factor, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,  that vertically transforms the polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e by scaling (1) the entire function and (2) only the leading coefficient (see figure below). To compare both cases, (1) and (2), find\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV0,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix that represents the vertex of the original polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix that represents the scaled vertex for case 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix that represents the scaled vertex for case 2;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1 \u0026lt;= m0, m1, m2 \u0026lt; n \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the degree of polynomial (see Hint). Return the first column of each matrix sorted by increasing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-values (in ascending order), while the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-value of the vertex in the second column. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint. The vertex of an even-degree polynomial is not necessarily unique, i.e., the global extremum may be reached at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, multiple distinct, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-values.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(p, k)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[V0, V1, V2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"310\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"265\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Comparing scales\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":61157,"title":"Scaling vertically parabola by evaluating its area over an interval","description":"Let p be a quadratic polynomial, with its axis of symmetry being the y-axis. Considering the vertical shift of its vertex to the origin, find the positive constant, k, that scales the shifted parabola such that its area over the interval [-a; a] (a\u003e0) will be equal to the area under the original parabola (see figure below).\r\ninput: (p, a)\r\noutput: k\r\n\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 447.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 223.9px; transform-origin: 408px 223.9px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be a quadratic polynomial, with its axis of symmetry being the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis. Considering the vertical shift of its vertex to the origin, find the positive constant, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, that scales the shifted parabola such that its area over the interval \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[-a; a] (a\u0026gt;0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be equal to the area under the original parabola (see figure below).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(p, a)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 255.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 127.9px; text-align: left; transform-origin: 384px 127.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"326\" height=\"250\" style=\"vertical-align: baseline;width: 326px;height: 250px\" src=\"data:image/png;base64,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\" alt=\"Scale parabola\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function k = scale_parabola(p, a)\r\n  k = x;\r\nend","test_suite":"%%\r\np = [1 0 1];\r\na = 2;\r\nk_correct = 7/4;\r\nassert(isapprox(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [1 0 -1];\r\na = 2;\r\nk_correct = 0.25;\r\nassert(isapprox(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [5 0 0];\r\na = 0.5;\r\nk_correct = 1;\r\nassert(isequal(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\nfiletext = fileread('scale_parabola.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [-3 0 1];\r\na = 1;\r\nk_correct = 0;\r\nassert(isequal(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [-3 0 2];\r\na = 1;\r\nk_correct = -1;\r\nassert(isequal(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [-3 0 2];\r\na = 3;\r\nk_correct = 7/9;\r\nassert(isapprox(scale_parabola(p,a),k_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-16T14:57:57.000Z","deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2026-01-16T14:57:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-10T14:36:03.000Z","updated_at":"2026-03-29T13:27:42.000Z","published_at":"2026-01-15T14:52:59.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be a quadratic polynomial, with its axis of symmetry being the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis. Considering the vertical shift of its vertex to the origin, find the positive constant, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, that scales the shifted parabola such that its area over the interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[-a; a] (a\u0026gt;0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be equal to the area under the original parabola (see figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(p, a)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"250\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"326\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Scale parabola\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60566,"title":"Given a Polyshape_01 (ps) Return its Perimeter, Area, and Centroid.","description":"Return the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\r\nReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\r\nReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 52.3333px; transform-origin: 407.5px 52.3333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.8333px; text-align: left; transform-origin: 384.5px 10.8333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21.6667px; text-align: left; transform-origin: 384.5px 21.6667px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.8333px; text-align: left; transform-origin: 384.5px 10.8333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"%%\r\nfunction [P, A, Cx, Cy] = PolyShape_01(ps)\r\n    % Return the perimeter (P) of a polyshape object, which is the sum\r\n    % of the lengths of its boundaries.\r\n    \r\n    % Return the total area (A) of a polyshape object, which is the sum\r\n    % of the areas of the solid regions that make up the polyshape.\r\n    \r\n    % Return the x-coordinate (Cx) and the y-coordinate (Cy) of the\r\n    % centroid of a polyshape. \r\n end","test_suite":"%% Test 1\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),1313))\r\n    assert(isequal(round(A,4),134508.0227))\r\n    assert(isequal(round(Cx,4),17))\r\n    assert(isequal(round(Cy,4),47))\r\n\r\n    \r\n%% Test 2\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),1313))\r\n    assert(isequal(round(A,4),134508.0227))\r\n    assert(isequal(round(Cx,4),254))\r\n    assert(isequal(round(Cy,4),-1676))\r\n\r\n    \r\n%% Test 3\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),177.255))\r\n    assert(isequal(round(A,4),2451.4087))\r\n    assert(isequal(round(Cx,4),34.29 ))\r\n    assert(isequal(round(Cy,4),-226.26))\r\n\r\n    \r\n%% Test 4\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),206.155))\r\n    assert(isequal(round(A,4),2385.7031))\r\n    assert(isequal(round(Cx,4),34.0501))\r\n    assert(isequal(round(Cy,4),-226.4324))\r\n\r\n    \r\n%% Test 5\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[20, -220],'SideLength', 1.7));\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),235.055))\r\n    assert(isequal(round(A,4),2319.9976))\r\n    assert(isequal(round(Cx,4),34.448))\r\n    assert(isequal(round(Cy,4),-226.6146))\r\n\r\n    \r\n%% Test 6\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[20, -220],'SideLength', 1.7));\r\n    ps = subtract(ps,polyshape([20 30.1 40.1 45.1 50 45.2 40.2 30.2 27.2],[-235 -239 -239 -237 -235 -239 -241 -240.5 -240]));\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),300.0489))\r\n    assert(isequal(round(A,4),2274.2476))\r\n    assert(isequal(round(Cx,4),34.4235))\r\n    assert(isequal(round(Cy,4),-226.367))\r\n    \r\n    \r\n    ","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":20795,"edited_by":20795,"edited_at":"2024-06-28T13:41:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-26T18:00:30.000Z","updated_at":"2026-03-18T15:16:22.000Z","published_at":"2024-06-26T18:18:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eReturn the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2447,"title":"Musical Note Interval 1 - Diatonic Scale","description":"Assuming a simple diatonic C scale, calculate the interval (integer) between two notes (provided as strings). By applying numbers to the notes of the scale (C,D,E,F,G,A,B,C = 1,2,3,4,5,6,7,8), intervals can be calculated. Because a unison is defined as one rather than zero, you add one to the numerical difference. The intervals are defined as:\r\n\r\nC - C: perfect unison, 1\r\n\r\nC - D: major second, 2\r\n\r\nC - E: major third, 3\r\n\r\nC - F: perfect fourth, 4\r\n\r\nC - G: perfect fifth, 5\r\n\r\nC - A: major sixth, 6\r\n\r\nC - B: major seventh, 7\r\n\r\nFor example, if the input is {'C','G'} the output will be a perfect fifth: 5-1+1=5. For input {'E','A'} the output will be a perfect fourth: 6-3+1=4.\r\n\r\nFor intervals that wrap around the scale, add seven to the resulting negative number to obtain the correct interval. For example, for {'A','C'} the output will be a major third: 1-6+1=-4, -4+7=3.","description_html":"\u003cp\u003eAssuming a simple diatonic C scale, calculate the interval (integer) between two notes (provided as strings). By applying numbers to the notes of the scale (C,D,E,F,G,A,B,C = 1,2,3,4,5,6,7,8), intervals can be calculated. Because a unison is defined as one rather than zero, you add one to the numerical difference. The intervals are defined as:\u003c/p\u003e\u003cp\u003eC - C: perfect unison, 1\u003c/p\u003e\u003cp\u003eC - D: major second, 2\u003c/p\u003e\u003cp\u003eC - E: major third, 3\u003c/p\u003e\u003cp\u003eC - F: perfect fourth, 4\u003c/p\u003e\u003cp\u003eC - G: perfect fifth, 5\u003c/p\u003e\u003cp\u003eC - A: major sixth, 6\u003c/p\u003e\u003cp\u003eC - B: major seventh, 7\u003c/p\u003e\u003cp\u003eFor example, if the input is {'C','G'} the output will be a perfect fifth: 5-1+1=5. For input {'E','A'} the output will be a perfect fourth: 6-3+1=4.\u003c/p\u003e\u003cp\u003eFor intervals that wrap around the scale, add seven to the resulting negative number to obtain the correct interval. For example, for {'A','C'} the output will be a major third: 1-6+1=-4, -4+7=3.\u003c/p\u003e","function_template":"function interval = note_interval(notes)\r\n interval = 0;\r\nend","test_suite":"%%\r\nnotes = {'C','G'};\r\ninterval = 5;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'C','E'};\r\ninterval = 3;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'G','C'};\r\ninterval = 4;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'C','B'};\r\ninterval = 7;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'C','C'};\r\ninterval = 1;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'E','A'};\r\ninterval = 4;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'D','C'};\r\ninterval = 7;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'D','E'};\r\ninterval = 2;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'A','C'};\r\ninterval = 3;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'C','A'};\r\ninterval = 6;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'C','E'};\r\ninterval = 3;\r\nassert(isequal(note_interval(notes),interval))\r\n\r\n%%\r\nnotes = {'E','C'};\r\ninterval = 6;\r\nassert(isequal(note_interval(notes),interval))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":42,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-07-18T15:06:07.000Z","updated_at":"2026-03-17T11:56:46.000Z","published_at":"2014-07-18T15:06:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssuming a simple diatonic C scale, calculate the interval (integer) between two notes (provided as strings). By applying numbers to the notes of the scale (C,D,E,F,G,A,B,C = 1,2,3,4,5,6,7,8), intervals can be calculated. Because a unison is defined as one rather than zero, you add one to the numerical difference. The intervals are defined as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eC - C: perfect unison, 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eC - D: major second, 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eC - E: major third, 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eC - F: perfect fourth, 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eC - G: perfect fifth, 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eC - A: major sixth, 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eC - B: major seventh, 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if the input is {'C','G'} the output will be a perfect fifth: 5-1+1=5. For input {'E','A'} the output will be a perfect fourth: 6-3+1=4.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor intervals that wrap around the scale, add seven to the resulting negative number to obtain the correct interval. For example, for {'A','C'} the output will be a major third: 1-6+1=-4, -4+7=3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61151,"title":"Scaling vertically functions","description":"Given a real function by the 1×n array, x, of inputs and the 1×n array, y, of outputs, consider shifting vertically its graph by the scale factor k (see figure below). Return\r\ny_scaled, which is the 1×n vector that stands for the outputs of the scaled function;\r\ns = 'strech' or 'compress', if the graph will be away from or towards the x-axis, respectively, becoming narrower or wider relative to the original function's graph. Return s = '', if there is no change in size;\r\nr = 'flip' or 'flat' if the graph will be reflected over the x-axis or collapses the entire graph onto the x-axis, respectively. Return r = '', if the orientation is preserved.\r\ninput: (x, y, k)\r\noutput: [y_scaled, s, r]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 489.987px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 244.988px; transform-origin: 408px 244.994px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a real function by the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of inputs and the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eof outputs, consider shifting vertically its graph by the scale factor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see figure below). Return\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.188px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 51.0875px; transform-origin: 391px 51.0938px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey_scaled\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e vector that stands for the outputs of the scaled function;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 'strech' or 'compress', if the graph will be away from or towards the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis, respectively, becoming narrower or wider relative to the original function's graph. Return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = '', if there is no change in size;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 'flip' or 'flat' if the graph will be reflected over the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis or collapses the entire graph onto the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis, respectively. Return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = '', if the orientation is preserved.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(x, y, k)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[y_scaled, s, r]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 255.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 127.9px; text-align: left; transform-origin: 384px 127.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"369\" height=\"250\" style=\"vertical-align: baseline;width: 369px;height: 250px\" src=\"data:image/png;base64,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\" alt=\"Scaling function's graph\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [y_scaled, s, r] = scaling(x,y,k)\r\n  y_scaled = x;\r\n  s = x;\r\n  r = x;\r\nend","test_suite":"%% \r\nx  = [0 1 2 5 10 15 20 25];\r\ny = [4 4.6 4.4 3.4 3.1 1.8 1.4 2];\r\nk = 2.62; \r\ny_correct = [10.48  12.052  11.528  8.908  8.122  4.716  3.668  5.24];\r\ns_correct = 'stretch';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -pi/2:pi/12:pi/2;\r\ny = sin(x).*cos(x);\r\nk = 2;\r\ny_correct = sin(2*x);\r\ns_correct = 'stretch';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -pi/2:pi/12:pi/2;\r\ny = 1 - cos(2*x);\r\nk = 0.5;\r\ny_correct = (sin(x)).^2;\r\ns_correct = 'compress';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -pi:pi/6:pi;\r\ny = (sin(x)).^2;\r\nk = - 1;\r\ny_correct = (cos(x)).^2 -1;\r\ns_correct = '';\r\nr_correct = 'flip';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -5:5;\r\ny = atan(x);\r\nk = 0;\r\ny_correct = 0.*x;\r\ns_correct = 'compress';\r\nr_correct = 'flat';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nfiletext = fileread('scaling.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = -2:0.5:2;\r\ny = polyval([1/3 0 -1 0], x);\r\nk = 3;\r\ny_correct = [-2 9/8 2 11/8 0 -11/8 -2 -9/8 2];\r\ns_correct = 'stretch';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(isequal(s, s_correct))\r\nassert(isequal(r, r_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-11T13:38:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-06T11:12:26.000Z","updated_at":"2026-03-28T12:45:32.000Z","published_at":"2026-01-11T13:38:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a real function by the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of inputs and the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eof outputs, consider shifting vertically its graph by the scale factor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see figure below). Return\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey_scaled\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e vector that stands for the outputs of the scaled function;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 'strech' or 'compress', if the graph will be away from or towards the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis, respectively, becoming narrower or wider relative to the original function's graph. Return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = '', if there is no change in size;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 'flip' or 'flat' if the graph will be reflected over the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis or collapses the entire graph onto the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis, respectively. Return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = '', if the orientation is preserved.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(x, y, k)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[y_scaled, s, r]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"250\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"369\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Scaling function's graph\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61164,"title":"Comparing to scale all terms versus one term of even-degree polynomial by the same scale factor","description":"Let p be an even-degree polynomial with positive leading coefficient. Consider the scale factor, k,  that vertically transforms the polynomial p by scaling (1) the entire function and (2) only the leading coefficient (see figure below). To compare both cases, (1) and (2), find\r\nV0, the m0×2 matrix that represents the vertex of the original polynomial p;\r\nV1, the m1×2 matrix that represents the scaled vertex for case 1:\r\nV2, the m2×2 matrix that represents the scaled vertex for case 2;\r\nwhere 1 \u003c= m0, m1, m2 \u003c n and n stands for the degree of polynomial (see Hint). Return the first column of each matrix sorted by increasing x-values (in ascending order), while the y-value of the vertex in the second column. \r\nHint. The vertex of an even-degree polynomial is not necessarily unique, i.e., the global extremum may be reached at m, multiple distinct, x-values.\r\ninput: (p, k)\r\noutput: [V0, V1, V2]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 611.112px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 305.55px; transform-origin: 469px 305.556px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 21px; text-align: left; transform-origin: 445px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be an even-degree polynomial with positive leading coefficient\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider the scale factor, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,  that vertically transforms the polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by scaling (1) the entire function and (2) only the leading coefficient (see figure below). To compare both cases, (1) and (2), find\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 452px 30.65px; transform-origin: 452px 30.6562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 424px 10.2125px; text-align: left; transform-origin: 424px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eV0,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix that represents the vertex of the original polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 424px 10.2125px; text-align: left; transform-origin: 424px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eV1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix that represents the scaled vertex for case 1:\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 424px 10.2125px; text-align: left; transform-origin: 424px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eV2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix that represents the scaled vertex for case 2;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 21px; text-align: left; transform-origin: 445px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1 \u0026lt;= m0, m1, m2 \u0026lt; n \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the degree of polynomial (see Hint). Return the first column of each matrix sorted by increasing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-values (in ascending order), while the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-value of the vertex in the second column. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 21px; text-align: left; transform-origin: 445px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint. The vertex of an even-degree polynomial is not necessarily unique, i.e., the global extremum may be reached at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, multiple distinct, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-values.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(p, k)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-style: italic; \"\u003e[V0, V1, V2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 315.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 157.9px; text-align: left; transform-origin: 445px 157.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"265\" height=\"310\" style=\"vertical-align: baseline;width: 265px;height: 310px\" src=\"data:image/png;base64,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\" alt=\"Comparing scales\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [V0, V1, V2] = vertices(p,k)\r\n  V0 = x;\r\n  V1 = x;\r\n  V2 = x;\r\nend","test_suite":"%%\r\np = [1 -4 -3];\r\nk = 5;\r\nV0_correct = [2 -7];\r\nV1_correct = [2 -35];\r\nV2_correct = [0.4 -3.8];\r\n[V0, V1, V2] = vertices(p,k);\r\nassert(isequal(V0,V0_correct))\r\nassert(isequal(V1,V1_correct))\r\nassert(isequal(V2,V2_correct))\r\n\r\n%%\r\np = [0.25 -1 -2 0 0];\r\nk = 4;\r\nV0_correct = [4 -32];\r\nV1_correct = [4 -128];\r\nV2_correct = [(3+sqrt(73))/8 -(827+73*sqrt(73))/2^9];\r\n[V0, V1, V2] = vertices(p,k);\r\nassert(isequal(V0,V0_correct))\r\nassert(isequal(V1,V1_correct))\r\ntolerance = 1e-13;\r\nassert(all(abs(V2 - V2_correct) \u003c tolerance))\r\n\r\n%%\r\np = [0.5 2.4 -3 -22 4.5 54 30.4];\r\nk = 5;\r\nV0_correct = [-1 -2];\r\nV1_correct = [-1 -10];\r\nV2_correct = [-0.901803848596367 -0.57405744023312];\r\n[V0, V1, V2] = vertices(p,k);\r\nassert(all(isapprox(V0,V0_correct), 'all'))\r\ntolerance = 1e-13;\r\nassert(all(abs(V1 - V1_correct) \u003c tolerance))\r\nassert(all(abs(V2 - V2_correct) \u003c tolerance))\r\n\r\n%%\r\nfiletext = fileread('vertices.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [3 0 0 0 1];\r\nk = 1/3;\r\nV0_correct = [0 1];\r\nV1_correct = [0 1/3];\r\nV2_correct = [0 1];\r\n[V0, V1, V2] = vertices(p,k);\r\nassert(isequal(V0,V0_correct))\r\nassert(all(isapprox(V1,V1_correct), 'all'))\r\nassert(isequal(V2,V2_correct))\r\n\r\n%%\r\np = [0.5 3 7.5 11 11 8 4];\r\nk = 10;\r\nV0_correct = [-2 0];\r\nV1_correct = [-2 0];\r\nV2_correct = [-0.590924701770178 1.75514977256519];\r\n[V0, V1, V2] = vertices(p,k);\r\ntolerance = 1e-13;\r\nassert(all(abs(V0 - V0_correct) \u003c tolerance))\r\nassert(all(abs(V1 - V1_correct) \u003c tolerance))\r\nassert(all(abs(V2 - V2_correct) \u003c tolerance))\r\n\r\n%%\r\np = [0.25 -2 1.5 10 0];\r\nk = 0.2;\r\nV0_correct = [-1 -6.25; 5 -6.25]; \r\nV1_correct = [-1 -1.25; 5 -1.25];\r\nV2_correct = [29.43264376174156 -11878.00773655344];\r\n[V0, V1, V2] = vertices(p,k);\r\nassert(all(isapprox(V0,V0_correct), 'all'))\r\nassert(all(isapprox(V0(1,:), V0_correct(1,:)), 'all'))\r\ntolerance1 = 1e-13;\r\nassert(all(abs(V1(2,:) - V1_correct(2,:)) \u003c tolerance1))\r\ntolerance = 1e-11;\r\nassert(all(abs(V2 - V2_correct) \u003c tolerance))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-04-02T17:08:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2026-04-02T17:08:16.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-14T14:02:53.000Z","updated_at":"2026-04-03T19:14:06.000Z","published_at":"2026-01-19T17:28:19.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be an even-degree polynomial with positive leading coefficient\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the scale factor, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,  that vertically transforms the polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e by scaling (1) the entire function and (2) only the leading coefficient (see figure below). To compare both cases, (1) and (2), find\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV0,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix that represents the vertex of the original polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix that represents the scaled vertex for case 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix that represents the scaled vertex for case 2;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1 \u0026lt;= m0, m1, m2 \u0026lt; n \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the degree of polynomial (see Hint). Return the first column of each matrix sorted by increasing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-values (in ascending order), while the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-value of the vertex in the second column. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint. The vertex of an even-degree polynomial is not necessarily unique, i.e., the global extremum may be reached at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, multiple distinct, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-values.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(p, k)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[V0, V1, V2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"310\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"265\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Comparing scales\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"scale\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"scale\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"scale\"","","\"","scale","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007effc5545648\u003e":null,"#\u003cMathWorks::Search::Field:0x00007effc55455a8\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007effc55447e8\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007effc55458c8\u003e":1,"#\u003cMathWorks::Search::Field:0x00007effc5545828\u003e":50,"#\u003cMathWorks::Search::Field:0x00007effc5545788\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007effc55456e8\u003e":"tag:\"scale\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007effc55456e8\u003e":"tag:\"scale\""},"queried_facets":{}},"query_backend":{"connection":{"configuration":{"index_url":"http://index-op-v2/solr/","query_url":"http://search-op-v2/solr/","direct_access_index_urls":["http://index-op-v2/solr/"],"direct_access_query_urls":["http://search-op-v2/solr/"],"timeout":10,"vhost":"search","exchange":"search.topic","heartbeat":30,"pre_index_mode":false,"host":"rabbitmq-eks","port":5672,"username":"cody-search","password":"78X075ddcV44","virtual_host":"search","indexer":"amqp","http_logging":"true","core":"cody"},"query_connection":{"uri":"http://search-op-v2/solr/cody/","proxy":null,"connection":{"parallel_manager":null,"headers":{"User-Agent":"Faraday v1.0.1"},"params":{},"options":{"params_encoder":"Faraday::FlatParamsEncoder","proxy":null,"bind":null,"timeout":null,"open_timeout":null,"read_timeout":null,"write_timeout":null,"boundary":null,"oauth":null,"context":null,"on_data":null},"ssl":{"verify":true,"ca_file":null,"ca_path":null,"verify_mode":null,"cert_store":null,"client_cert":null,"client_key":null,"certificate":null,"private_key":null,"verify_depth":null,"version":null,"min_version":null,"max_version":null},"default_parallel_manager":null,"builder":{"adapter":{"name":"Faraday::Adapter::NetHttp","args":[],"block":null},"handlers":[{"name":"Faraday::Response::RaiseError","args":[],"block":null}],"app":{"app":{"ssl_cert_store":{"verify_callback":null,"error":null,"error_string":null,"chain":null,"time":null},"app":{},"connection_options":{},"config_block":null}}},"url_prefix":"http://search-op-v2/solr/cody/","manual_proxy":false,"proxy":null},"update_format":"RSolr::JSON::Generator","update_path":"update","options":{"url":"http://search-op-v2/solr/cody"}}},"query":{"params":{"per_page":50,"term":"tag:\"scale\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"scale\"","","\"","scale","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007effc5545648\u003e":null,"#\u003cMathWorks::Search::Field:0x00007effc55455a8\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007effc55447e8\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007effc55458c8\u003e":1,"#\u003cMathWorks::Search::Field:0x00007effc5545828\u003e":50,"#\u003cMathWorks::Search::Field:0x00007effc5545788\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007effc55456e8\u003e":"tag:\"scale\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007effc55456e8\u003e":"tag:\"scale\""},"queried_facets":{}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":61157,"difficulty_rating":"easy"},{"id":60566,"difficulty_rating":"easy"},{"id":2447,"difficulty_rating":"easy"},{"id":61151,"difficulty_rating":"easy"},{"id":61164,"difficulty_rating":"medium"}]}}