{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","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":"2025-12-14T00:00:00.000Z","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":42987,"title":"Roots of a quadratic equation.","description":"Calculate the roots of a quadratic equation, given coefficients a, b, and c, for the equation a*x^2 + b*x + c = 0.","description_html":"\u003cp\u003eCalculate the roots of a quadratic equation, given coefficients a, b, and c, for the equation a*x^2 + b*x + c = 0.\u003c/p\u003e","function_template":"function y = quadRoots(a,b,c)\r\n  y = a;\r\nend","test_suite":"%%\r\na=1;\r\nb=2;\r\nc=1;\r\ny_correct = [-1 -1];\r\nassert(norm(quadRoots(a,b,c)-y_correct) \u003c 10*eps)\r\n\r\n%%\r\na=1;\r\nb=-5;\r\nc=6;\r\ny_correct = [2 3];\r\nassert(norm(quadRoots(a,b,c)-y_correct) \u003c 10*eps)\r\n\r\n%%\r\na=1;\r\nb=5;\r\nc=6;\r\ny_correct = [-3 -2];\r\nassert(norm(quadRoots(a,b,c)-y_correct) \u003c 10*eps)\r\n\r\n%%\r\na=2;\r\nb=10;\r\nc=12;\r\ny_correct = [-3 -2];\r\nassert(norm(quadRoots(a,b,c)-y_correct) \u003c 10*eps)\r\n\r\n%%\r\na=1;\r\nb=19;\r\nc=90;\r\ny_correct = [-10 -9];\r\nassert(norm(quadRoots(a,b,c)-y_correct) \u003c 100*eps)\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":6,"created_by":91311,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":73,"test_suite_updated_at":"2016-10-02T01:45:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-09-16T10:45:13.000Z","updated_at":"2026-02-13T18:45:17.000Z","published_at":"2016-09-16T10:45:13.000Z","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\u003eCalculate the roots of a quadratic equation, given coefficients a, b, and c, for the equation a*x^2 + b*x + c = 0.\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":42840,"title":"Coefficients and vertex of a parabola given 3 points","description":"Given 3 points, each defined by x and y, compute the coefficients: [a,b,c] of a parabola with equation: y = ax^2 + bx + c passing through those points.  Also solve for the location of its vertex: [xv,yv].\r\n\r\nExample:\r\n\r\n Inputs:  D = [0 3]; E = [1 6]; F = [-1 2]\r\n Outputs: C = [1 2 3]; V = [-1 2]\r\n Hence, the quadratic equation is: y = x^2 +2x + 3, with vertex at (-1,2)","description_html":"\u003cp\u003eGiven 3 points, each defined by x and y, compute the coefficients: [a,b,c] of a parabola with equation: y = ax^2 + bx + c passing through those points.  Also solve for the location of its vertex: [xv,yv].\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e Inputs:  D = [0 3]; E = [1 6]; F = [-1 2]\r\n Outputs: C = [1 2 3]; V = [-1 2]\r\n Hence, the quadratic equation is: y = x^2 +2x + 3, with vertex at (-1,2)\u003c/pre\u003e","function_template":"function [Coeff,VERT] = Para3(P,Q,R)\r\nCoeff = [P,Q,R];\r\nVERT = [P,Q,R];\r\nend","test_suite":"%%\r\nP1 = [1 0]; P2 = [2 5]; P3 = [-1 2];\r\nabc = [2 -1 -1];\r\nO1 = Para3(P1,P2,P3);\r\nassert(isequal(O1,abc))\r\n\r\n%%\r\nP1 = [1 0]; P2 = [2 5]; P3 = [-1 2];\r\nvxvy = [0.25 -1.125];\r\n[~,O2] = Para3(P1,P2,P3);\r\nassert(isequal(O2,vxvy))\r\n\r\n%%\r\ni = [0 0]; j = [1 1]; k = [-1 1];\r\nabc = [1 0 0];\r\ntip = [0 0];\r\n[Res,Ans] = Para3(i,j,k);\r\nassert(isequal(Res,abc))\r\nassert(isequal(Ans,tip))\r\n\r\n%%\r\nptA = [-1 -5]; ptB = [2 4]; ptC = [3 -5];\r\nexp1 = [-3 6 4];\r\nexp2 = [1 7];\r\n[coefficients,vertex] = Para3(ptA,ptB,ptC);\r\nassert(isequal(exp1,coefficients))\r\nassert(isequal(exp2,vertex))","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":54708,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2016-05-01T20:20:27.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2016-04-29T14:32:30.000Z","updated_at":"2026-01-20T14:47:31.000Z","published_at":"2016-04-29T14:58:42.000Z","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\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"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\\n\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\u003eGiven 3 points, each defined by x and y, compute the coefficients: [a,b,c] of a parabola with equation: y = ax^2 + bx + c passing through those points. Also solve for the location of its vertex: [xv,yv].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Inputs:  D = [0 3]; E = [1 6]; F = [-1 2]\\n Outputs: C = [1 2 3]; V = [-1 2]\\n Hence, the quadratic equation is: y = x^2 +2x + 3, with vertex at (-1,2)]]\u003e\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":486,"title":"Surface Fit z(x,y)","description":"Given three vectors x,y,z. Find four coefficients c = [cxx cxy cyy c00], such that z = cxx*x.^2+cxy*x.*y+cyy*y.^2+c00. \r\n\r\nFor example,\r\n\r\n x = [ 0  0  1  1  2  2  3  3]\r\n y = [ 0  1  0  1  0  1  0  1]\r\n z = [-4 -1 -3 -2  0 -1  5  2]\r\n\r\nthen\r\n\r\n z = x.^2-2*x.*y+3*y.^2-4 \r\n\r\nand\r\n\r\n c = [cxx cxy cyy c00] = [1 -2 3 -4]","description_html":"\u003cp\u003eGiven three vectors x,y,z. Find four coefficients c = [cxx cxy cyy c00], such that z = cxx*x.^2+cxy*x.*y+cyy*y.^2+c00.\u003c/p\u003e\u003cp\u003eFor example,\u003c/p\u003e\u003cpre\u003e x = [ 0  0  1  1  2  2  3  3]\r\n y = [ 0  1  0  1  0  1  0  1]\r\n z = [-4 -1 -3 -2  0 -1  5  2]\u003c/pre\u003e\u003cp\u003ethen\u003c/p\u003e\u003cpre\u003e z = x.^2-2*x.*y+3*y.^2-4 \u003c/pre\u003e\u003cp\u003eand\u003c/p\u003e\u003cpre\u003e c = [cxx cxy cyy c00] = [1 -2 3 -4]\u003c/pre\u003e","function_template":"function c = sufit(x,y,z)\r\n  cxx=0;\r\n  cxy=0;\r\n  cyy=0;\r\n  c00=0;\r\n  c=[cxx cxy cyy c00];\r\nend","test_suite":"%%\r\nx= [0 0 1 1 2 2 3 3];\r\ny= [0 1 0 1 0 1 0 1];\r\nz=[-4 -1 -3 -2 0 -1 5 2];\r\nc=[1 -2 3 -4]; \r\nassert(isequal(c,round(sufit(x,y,z))))\r\n%%\r\nx= rand(1,100);\r\ny= rand(1,100);\r\nz=7*x.^2-9*x.*y+11*y.^2-17;\r\nc=[7 -9 11 -17]; \r\nassert(isequal(c,round(sufit(x,y,z))))\r\n%%\r\nx= rand(1,10000);\r\ny= rand(1,10000);\r\nz=17*x.^2-19*x.*y+11*y.^2-13;\r\nc=[17 -19 11 -13]; \r\nassert(isequal(c,round(sufit(x,y,z))))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":46,"test_suite_updated_at":"2012-03-12T19:23:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-12T17:50:33.000Z","updated_at":"2025-12-07T17:59:24.000Z","published_at":"2012-03-19T09:01:03.000Z","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\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"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\\n\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\u003eGiven three vectors x,y,z. Find four coefficients c = [cxx cxy cyy c00], such that z = cxx*x.^2+cxy*x.*y+cyy*y.^2+c00.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = [ 0  0  1  1  2  2  3  3]\\n y = [ 0  1  0  1  0  1  0  1]\\n z = [-4 -1 -3 -2  0 -1  5  2]]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ z = x.^2-2*x.*y+3*y.^2-4]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ c = [cxx cxy cyy c00] = [1 -2 3 -4]]]\u003e\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":61143,"title":"Translating parabola by its vertex to the origin","description":"Given a quadratic polynomial, p(x) = ax^2 + bx + c (a ~= 0), represented by the vector [a b c], consider the translation of the parabola by shifting its vertex to the origin (see figure below).\r\nFind \r\nd (d\u003e0) the shifting distance of the above translation;\r\nv the vertical shift, which stands for 'up' and 'down' if the parabola is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\r\nh the horizontal shift, which stands for 'right' and 'left' if the parabola is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\r\nHint: Be careful to the potential computer errors whenever the results will be integer numbers.\r\ninput: p\r\noutput: [d, v, h]\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: 633.987px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 316.987px; transform-origin: 408px 316.994px; 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 quadratic 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(x) = ax^2 + bx + c (a ~= 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, represented by the vector \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 b c]\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, consider the translation of the parabola by shifting its vertex to the origin (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=\"\"\u003eFind \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; \"\u003ed (d\u0026gt;0)\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 shifting distance of the above translation;\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; \"\u003ev\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 vertical shift, which stands for 'up' and 'down' if the parabola is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\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; \"\u003eh\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 horizontal shift, which stands for 'right' and 'left' if the parabola is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\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=\"\"\u003eHint: Be careful to the potential computer errors whenever the results will be integer numbers.\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=\"\"\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; \"\u003ep\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[d, v, 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alt=\"Shift parabola\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [d, v, h] = shift_parabola(p)\r\n  d = x;\r\n  v = x;\r\n  h = x;\r\nend","test_suite":"%%\r\np = [-1 12 -28];\r\nd_correct = 10;\r\nv_correct = 'down';\r\nh_correct = 'left';\r\n[d, v, h] = shift_parabola(p);\r\nassert(isequal(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%% \r\np = [1 -3 0.25];\r\nd_correct = 2.5;\r\nv_correct = 'up';\r\nh_correct = 'left';\r\n[d, v, h] = shift_parabola(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%% \r\np = [4 -12 9];\r\nd_correct = 1.5;\r\nv_correct = '';\r\nh_correct = 'left';\r\n[d, v, h] = shift_parabola(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\nfiletext = fileread('shift_parabola.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [-5 -2 -1.6];\r\nd_correct = sqrt(2);\r\nv_correct = 'up';\r\nh_correct = 'right';\r\n[d, v, h] = shift_parabola(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [-5 -2 1.2];\r\nd_correct = sqrt(2);\r\nv_correct = 'down';\r\nh_correct = 'right';\r\n[d, v, h] = shift_parabola(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":3,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-03T10:31:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2026-01-03T10:31:42.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-12-24T12:38:12.000Z","updated_at":"2026-02-27T10:20:46.000Z","published_at":"2026-01-02T10:06:27.000Z","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 quadratic 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(x) = ax^2 + bx + c (a ~= 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, represented by the vector \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 b c]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, consider the translation of the parabola by shifting its vertex to the origin (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:t\u003eFind \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\u003ed (d\u0026gt;0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the shifting distance of the above translation;\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\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the vertical shift, which stands for 'up' and 'down' if the parabola is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\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\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the horizontal shift, which stands for 'right' and 'left' if the parabola is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\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: Be careful to the potential computer errors whenever the results will be integer numbers.\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 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equation","description":"A conic of revolution (around the |z| axis) can be defined by the equation\r\n\r\n   s^2 – 2*R*z + (k+1)*z^2 = 0\r\n\r\nwhere |s^2=x^2+y^2|, |R| is the vertex radius of curvature, and |k| is the conic constant: |k\u003c-1| for a hyperbola, |k=-1| for a parabola, |-1\u003ck\u003c0| for a tall ellipse, |k=0| for a sphere, and |k\u003e0| for a short ellipse.\r\n\r\nWrite a function |z=conic(s,R,k)| to calculate height |z| as a function of radius |s| for given |R| and |k|.  Choose the branch of the solution that gives |z=s^2/(2*R)+...| for small values of |s|.  This defines a concave surface for |R\u003e0| and a convex surface for |R\u003c0|.  \r\n\r\nThe trick is to get full machine precision for all values of |s| and |R|.  The test suite will require a relative error less than |4*eps|, where |eps| is the machine precision.\r\n\r\nHint (added 2015/09/03): the straightforward solution is \r\n\r\n   z = (R-sqrt(R^2-(k+1)*s^2))/(k+1), \r\n\r\nbut this does not work if |k=-1|, gives the wrong branch of the solution if |R\u003c0|, and is subject to severe roundoff error if |s^2| is small compared to |R^2|.  It is possible, however, to find a mathematically equivalent form of the solution that solves all three problems at once.\r\n","description_html":"\u003cp\u003eA conic of revolution (around the \u003ctt\u003ez\u003c/tt\u003e axis) can be defined by the equation\u003c/p\u003e\u003cpre\u003e   s^2 – 2*R*z + (k+1)*z^2 = 0\u003c/pre\u003e\u003cp\u003ewhere \u003ctt\u003es^2=x^2+y^2\u003c/tt\u003e, \u003ctt\u003eR\u003c/tt\u003e is the vertex radius of curvature, and \u003ctt\u003ek\u003c/tt\u003e is the conic constant: \u003ctt\u003ek\u0026lt;-1\u003c/tt\u003e for a hyperbola, \u003ctt\u003ek=-1\u003c/tt\u003e for a parabola, \u003ctt\u003e-1\u0026lt;k\u0026lt;0\u003c/tt\u003e for a tall ellipse, \u003ctt\u003ek=0\u003c/tt\u003e for a sphere, and \u003ctt\u003ek\u0026gt;0\u003c/tt\u003e for a short ellipse.\u003c/p\u003e\u003cp\u003eWrite a function \u003ctt\u003ez=conic(s,R,k)\u003c/tt\u003e to calculate height \u003ctt\u003ez\u003c/tt\u003e as a function of radius \u003ctt\u003es\u003c/tt\u003e for given \u003ctt\u003eR\u003c/tt\u003e and \u003ctt\u003ek\u003c/tt\u003e.  Choose the branch of the solution that gives \u003ctt\u003ez=s^2/(2*R)+...\u003c/tt\u003e for small values of \u003ctt\u003es\u003c/tt\u003e.  This defines a concave surface for \u003ctt\u003eR\u0026gt;0\u003c/tt\u003e and a convex surface for \u003ctt\u003eR\u0026lt;0\u003c/tt\u003e.\u003c/p\u003e\u003cp\u003eThe trick is to get full machine precision for all values of \u003ctt\u003es\u003c/tt\u003e and \u003ctt\u003eR\u003c/tt\u003e.  The test suite will require a relative error less than \u003ctt\u003e4*eps\u003c/tt\u003e, where \u003ctt\u003eeps\u003c/tt\u003e is the machine precision.\u003c/p\u003e\u003cp\u003eHint (added 2015/09/03): the straightforward solution is\u003c/p\u003e\u003cpre\u003e   z = (R-sqrt(R^2-(k+1)*s^2))/(k+1), \u003c/pre\u003e\u003cp\u003ebut this does not work if \u003ctt\u003ek=-1\u003c/tt\u003e, gives the wrong branch of the solution if \u003ctt\u003eR\u0026lt;0\u003c/tt\u003e, and is subject to severe roundoff error if \u003ctt\u003es^2\u003c/tt\u003e is small compared to \u003ctt\u003eR^2\u003c/tt\u003e.  It is possible, however, to find a mathematically equivalent form of the solution that solves all three problems at once.\u003c/p\u003e","function_template":"function z=conic(s,R,k)\r\nz=0;\r\nend","test_suite":"%%\r\nR=5;\r\nk=-1;\r\ns=-5:5;\r\nz=[25 16 9 4 1 0 1 4 9 16 25]/10;\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=-5;\r\nk=-1;\r\ns=-5:5;\r\nz=-[25 16 9 4 1 0 1 4 9 16 25]/10;\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=6;\r\nk=0;\r\ns=0:0.125:2;\r\nz=[0 0.001302224649086391 0.005210595859100573 ...\r\n   0.01173021649825800 0.02086962844930099 ...\r\n   0.03264086885999461 0.04705955010467117 ...\r\n   0.06414496470811713 0.08392021690038396 ...\r\n   0.1064123829368584 0.1316527028472488 ...\r\n   0.1596768068881667 0.1905249806888747 ...\r\n   0.2242424739260392 0.2608798583755018 ...\r\n   0.3004934424110011 0.3431457505076198];\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=6800;\r\nk=-2;\r\ns=10.^(-9:9);\r\nz=[7.352941176470588e-23 7.352941176470588e-21 ...\r\n   7.352941176470588e-19 7.352941176470588e-17 ...\r\n   7.352941176470588e-15 7.352941176470588e-13 ...\r\n   7.352941176470548e-11 7.352941176466613e-9 ...\r\n   7.352941176073046e-7 0.00007352941136716365 ...\r\n   0.007352937201052538 0.7352543677216725 ...\r\n   73.13611097583313 5292.973166264779 93430.93334894173 ...\r\n   993223.1197327390 9.993202311999733e6 9.99932002312e7 ...\r\n   9.9999320002312e8];\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=exp(1);\r\nk=pi;\r\ns=10.^(-7:0);\r\nz=[1.839397205857214e-15 1.839397205857469e-13 ...\r\n   1.839397205882986e-11 1.839397208434684e-09 ...\r\n   1.839397463604480e-07 0.00001839422981299153 ...\r\n   0.001841981926630790 0.2212216213343403];\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nt=fileread('conic.m');\r\nassert(isempty(findstr(t,'roots')))\r\nassert(isempty(findstr(t,'fzero')))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":245,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":37,"created_at":"2015-08-26T21:39:35.000Z","updated_at":"2026-02-08T12:47:36.000Z","published_at":"2015-08-26T22:21:10.000Z","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\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"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\\n\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\u003eA conic of revolution (around the\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e axis) can be defined by the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   s^2 – 2*R*z + (k+1)*z^2 = 0]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es^2=x^2+y^2\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:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the vertex radius of curvature, and\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the conic constant:\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u0026lt;-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a hyperbola,\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek=-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a parabola,\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-1\u0026lt;k\u0026lt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a tall ellipse,\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek=0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a sphere, and\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u0026gt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a short ellipse.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez=conic(s,R,k)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to calculate height\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as a function of radius\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for given\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Choose the branch of the solution that gives\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez=s^2/(2*R)+...\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for small values of\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. This defines a concave surface for\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u0026gt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and a convex surface for\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u0026lt;0\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=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe trick is to get full machine precision for all values of\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The test suite will require a relative error less than\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e4*eps\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eeps\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the machine precision.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint (added 2015/09/03): the straightforward solution is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   z = (R-sqrt(R^2-(k+1)*s^2))/(k+1),]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebut this does not work if\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek=-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, gives the wrong branch of the solution if\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u0026lt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and is subject to severe roundoff error if\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is small compared to\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. It is possible, however, to find a mathematically equivalent form of the solution that solves all three problems at once.\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\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":42987,"title":"Roots of a quadratic equation.","description":"Calculate the roots of a quadratic equation, given coefficients a, b, and c, for the equation a*x^2 + b*x + c = 0.","description_html":"\u003cp\u003eCalculate the roots of a quadratic equation, given coefficients a, b, and c, for the equation a*x^2 + b*x + c = 0.\u003c/p\u003e","function_template":"function y = quadRoots(a,b,c)\r\n  y = a;\r\nend","test_suite":"%%\r\na=1;\r\nb=2;\r\nc=1;\r\ny_correct = [-1 -1];\r\nassert(norm(quadRoots(a,b,c)-y_correct) \u003c 10*eps)\r\n\r\n%%\r\na=1;\r\nb=-5;\r\nc=6;\r\ny_correct = [2 3];\r\nassert(norm(quadRoots(a,b,c)-y_correct) \u003c 10*eps)\r\n\r\n%%\r\na=1;\r\nb=5;\r\nc=6;\r\ny_correct = [-3 -2];\r\nassert(norm(quadRoots(a,b,c)-y_correct) \u003c 10*eps)\r\n\r\n%%\r\na=2;\r\nb=10;\r\nc=12;\r\ny_correct = [-3 -2];\r\nassert(norm(quadRoots(a,b,c)-y_correct) \u003c 10*eps)\r\n\r\n%%\r\na=1;\r\nb=19;\r\nc=90;\r\ny_correct = [-10 -9];\r\nassert(norm(quadRoots(a,b,c)-y_correct) \u003c 100*eps)\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":6,"created_by":91311,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":73,"test_suite_updated_at":"2016-10-02T01:45:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-09-16T10:45:13.000Z","updated_at":"2026-02-13T18:45:17.000Z","published_at":"2016-09-16T10:45:13.000Z","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\u003eCalculate the roots of a quadratic equation, given coefficients a, b, and c, for the equation a*x^2 + b*x + c = 0.\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":42840,"title":"Coefficients and vertex of a parabola given 3 points","description":"Given 3 points, each defined by x and y, compute the coefficients: [a,b,c] of a parabola with equation: y = ax^2 + bx + c passing through those points.  Also solve for the location of its vertex: [xv,yv].\r\n\r\nExample:\r\n\r\n Inputs:  D = [0 3]; E = [1 6]; F = [-1 2]\r\n Outputs: C = [1 2 3]; V = [-1 2]\r\n Hence, the quadratic equation is: y = x^2 +2x + 3, with vertex at (-1,2)","description_html":"\u003cp\u003eGiven 3 points, each defined by x and y, compute the coefficients: [a,b,c] of a parabola with equation: y = ax^2 + bx + c passing through those points.  Also solve for the location of its vertex: [xv,yv].\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e Inputs:  D = [0 3]; E = [1 6]; F = [-1 2]\r\n Outputs: C = [1 2 3]; V = [-1 2]\r\n Hence, the quadratic equation is: y = x^2 +2x + 3, with vertex at (-1,2)\u003c/pre\u003e","function_template":"function [Coeff,VERT] = Para3(P,Q,R)\r\nCoeff = [P,Q,R];\r\nVERT = [P,Q,R];\r\nend","test_suite":"%%\r\nP1 = [1 0]; P2 = [2 5]; P3 = [-1 2];\r\nabc = [2 -1 -1];\r\nO1 = Para3(P1,P2,P3);\r\nassert(isequal(O1,abc))\r\n\r\n%%\r\nP1 = [1 0]; P2 = [2 5]; P3 = [-1 2];\r\nvxvy = [0.25 -1.125];\r\n[~,O2] = Para3(P1,P2,P3);\r\nassert(isequal(O2,vxvy))\r\n\r\n%%\r\ni = [0 0]; j = [1 1]; k = [-1 1];\r\nabc = [1 0 0];\r\ntip = [0 0];\r\n[Res,Ans] = Para3(i,j,k);\r\nassert(isequal(Res,abc))\r\nassert(isequal(Ans,tip))\r\n\r\n%%\r\nptA = [-1 -5]; ptB = [2 4]; ptC = [3 -5];\r\nexp1 = [-3 6 4];\r\nexp2 = [1 7];\r\n[coefficients,vertex] = Para3(ptA,ptB,ptC);\r\nassert(isequal(exp1,coefficients))\r\nassert(isequal(exp2,vertex))","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":54708,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2016-05-01T20:20:27.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2016-04-29T14:32:30.000Z","updated_at":"2026-01-20T14:47:31.000Z","published_at":"2016-04-29T14:58:42.000Z","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\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"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\\n\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\u003eGiven 3 points, each defined by x and y, compute the coefficients: [a,b,c] of a parabola with equation: y = ax^2 + bx + c passing through those points. Also solve for the location of its vertex: [xv,yv].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Inputs:  D = [0 3]; E = [1 6]; F = [-1 2]\\n Outputs: C = [1 2 3]; V = [-1 2]\\n Hence, the quadratic equation is: y = x^2 +2x + 3, with vertex at (-1,2)]]\u003e\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":486,"title":"Surface Fit z(x,y)","description":"Given three vectors x,y,z. Find four coefficients c = [cxx cxy cyy c00], such that z = cxx*x.^2+cxy*x.*y+cyy*y.^2+c00. \r\n\r\nFor example,\r\n\r\n x = [ 0  0  1  1  2  2  3  3]\r\n y = [ 0  1  0  1  0  1  0  1]\r\n z = [-4 -1 -3 -2  0 -1  5  2]\r\n\r\nthen\r\n\r\n z = x.^2-2*x.*y+3*y.^2-4 \r\n\r\nand\r\n\r\n c = [cxx cxy cyy c00] = [1 -2 3 -4]","description_html":"\u003cp\u003eGiven three vectors x,y,z. Find four coefficients c = [cxx cxy cyy c00], such that z = cxx*x.^2+cxy*x.*y+cyy*y.^2+c00.\u003c/p\u003e\u003cp\u003eFor example,\u003c/p\u003e\u003cpre\u003e x = [ 0  0  1  1  2  2  3  3]\r\n y = [ 0  1  0  1  0  1  0  1]\r\n z = [-4 -1 -3 -2  0 -1  5  2]\u003c/pre\u003e\u003cp\u003ethen\u003c/p\u003e\u003cpre\u003e z = x.^2-2*x.*y+3*y.^2-4 \u003c/pre\u003e\u003cp\u003eand\u003c/p\u003e\u003cpre\u003e c = [cxx cxy cyy c00] = [1 -2 3 -4]\u003c/pre\u003e","function_template":"function c = sufit(x,y,z)\r\n  cxx=0;\r\n  cxy=0;\r\n  cyy=0;\r\n  c00=0;\r\n  c=[cxx cxy cyy c00];\r\nend","test_suite":"%%\r\nx= [0 0 1 1 2 2 3 3];\r\ny= [0 1 0 1 0 1 0 1];\r\nz=[-4 -1 -3 -2 0 -1 5 2];\r\nc=[1 -2 3 -4]; \r\nassert(isequal(c,round(sufit(x,y,z))))\r\n%%\r\nx= rand(1,100);\r\ny= rand(1,100);\r\nz=7*x.^2-9*x.*y+11*y.^2-17;\r\nc=[7 -9 11 -17]; \r\nassert(isequal(c,round(sufit(x,y,z))))\r\n%%\r\nx= rand(1,10000);\r\ny= rand(1,10000);\r\nz=17*x.^2-19*x.*y+11*y.^2-13;\r\nc=[17 -19 11 -13]; \r\nassert(isequal(c,round(sufit(x,y,z))))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":46,"test_suite_updated_at":"2012-03-12T19:23:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-12T17:50:33.000Z","updated_at":"2025-12-07T17:59:24.000Z","published_at":"2012-03-19T09:01:03.000Z","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\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"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\\n\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\u003eGiven three vectors x,y,z. Find four coefficients c = [cxx cxy cyy c00], such that z = cxx*x.^2+cxy*x.*y+cyy*y.^2+c00.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = [ 0  0  1  1  2  2  3  3]\\n y = [ 0  1  0  1  0  1  0  1]\\n z = [-4 -1 -3 -2  0 -1  5  2]]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ z = x.^2-2*x.*y+3*y.^2-4]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ c = [cxx cxy cyy c00] = [1 -2 3 -4]]]\u003e\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":61143,"title":"Translating parabola by its vertex to the origin","description":"Given a quadratic polynomial, p(x) = ax^2 + bx + c (a ~= 0), represented by the vector [a b c], consider the translation of the parabola by shifting its vertex to the origin (see figure below).\r\nFind \r\nd (d\u003e0) the shifting distance of the above translation;\r\nv the vertical shift, which stands for 'up' and 'down' if the parabola is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\r\nh the horizontal shift, which stands for 'right' and 'left' if the parabola is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\r\nHint: Be careful to the potential computer errors whenever the results will be integer numbers.\r\ninput: p\r\noutput: [d, v, h]\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: 633.987px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 316.987px; transform-origin: 408px 316.994px; 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 quadratic 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(x) = ax^2 + bx + c (a ~= 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, represented by the vector \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 b c]\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, consider the translation of the parabola by shifting its vertex to the origin (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=\"\"\u003eFind \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; \"\u003ed (d\u0026gt;0)\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 shifting distance of the above translation;\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; \"\u003ev\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 vertical shift, which stands for 'up' and 'down' if the parabola is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\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; \"\u003eh\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 horizontal shift, which stands for 'right' and 'left' if the parabola is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\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=\"\"\u003eHint: Be careful to the potential computer errors whenever the results will be integer numbers.\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=\"\"\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; \"\u003ep\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[d, v, h]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 339.8px; 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 169.9px; text-align: left; transform-origin: 384px 169.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"480\" height=\"334\" style=\"vertical-align: baseline;width: 480px;height: 334px\" 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alt=\"Shift parabola\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [d, v, h] = shift_parabola(p)\r\n  d = x;\r\n  v = x;\r\n  h = x;\r\nend","test_suite":"%%\r\np = [-1 12 -28];\r\nd_correct = 10;\r\nv_correct = 'down';\r\nh_correct = 'left';\r\n[d, v, h] = shift_parabola(p);\r\nassert(isequal(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%% \r\np = [1 -3 0.25];\r\nd_correct = 2.5;\r\nv_correct = 'up';\r\nh_correct = 'left';\r\n[d, v, h] = shift_parabola(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%% \r\np = [4 -12 9];\r\nd_correct = 1.5;\r\nv_correct = '';\r\nh_correct = 'left';\r\n[d, v, h] = shift_parabola(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\nfiletext = fileread('shift_parabola.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [-5 -2 -1.6];\r\nd_correct = sqrt(2);\r\nv_correct = 'up';\r\nh_correct = 'right';\r\n[d, v, h] = shift_parabola(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [-5 -2 1.2];\r\nd_correct = sqrt(2);\r\nv_correct = 'down';\r\nh_correct = 'right';\r\n[d, v, h] = shift_parabola(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":3,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-03T10:31:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2026-01-03T10:31:42.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-12-24T12:38:12.000Z","updated_at":"2026-02-27T10:20:46.000Z","published_at":"2026-01-02T10:06:27.000Z","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 quadratic 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(x) = ax^2 + bx + c (a ~= 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, represented by the vector \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 b c]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, consider the translation of the parabola by shifting its vertex to the origin (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:t\u003eFind \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\u003ed (d\u0026gt;0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the shifting distance of the above translation;\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\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the vertical shift, which stands for 'up' and 'down' if the parabola is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\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\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the horizontal shift, which stands for 'right' and 'left' if the parabola is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\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: Be careful to the potential computer errors whenever the results will be integer numbers.\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 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SfM7xpHYzvSM4CJ0jTxf/7P1Ouvn5WhpUbx2hNns79Qr+iIRvNf0ZFafSiTvX6+CaEZgGoKOisqw+8X999vvZTT3i6efropy49DegYwIXJHXDhsvj5GK7oi0AujIxGL8UnyXYVbdNErNDIUZwOAOgo9KyogwyGFWSI9Axgn+WpXakuN3FrRFUFzs3jppbErOnw+EQ7nZ9HFVKFBQ1YACspyVizQadd205tD60pKurL8u6RnADnLsDVw/K3oCi2bio54PD+LLlRoAFBflrOi3APt0qVoY2O7q69uzfJvkZ4B5CDz1kAZGpXLzSbGDdiZF12iUbcuugDAqOxnRZeS//rsy+tIzwCyJUs1LHPzgw8OvvbaO6rnZqNsFl0iEXcvugDAqCyPdHWpnO5fpGcAY9NPP7EscXb2TJvloosHuqICgBBZzIqeR3oGkEm6EmfltgZOkH63SLcN29gV1b3tnABgROpSNIeBn0d6BmAtQ4mzulsDx03TRjbHjNkx33hsIQC4nh6jcR7pGYAFmSQdvDUwe/rB2ukaM425s5ByDgCu555JPw9IzwDMMnRx7ux00RRqXF1PTcCyZ7N81TLzzkLKOQAglXtnRdIzgBEyTPp8bi9xFobqC8tMrP+D9TV247GF6ZaiKecAACP3zoqkZwBCZCzViMXcVeIsu4dYLorIf22GAwIzt3MyducAAC+TzaFdOiuSngGvy3zgdmen647Ma2szXzEerJ1Nu3xjO6dUlEQDgJHrZkXSM+BdmbvRyRVYlzMWaeT6LGHMcg654tLQwIGFALwlGs00K9bWOn1WJD0DHiX7TGToRudmiUTSU4QJVqXo5RyW69bt7ZlqRQDAfTLPim+/7fRZkfQMeI5+4HZqqUYs5q5udBnkfWldr5lOV87h3g00AGDBvbMi6RnwkDFLNbIp+kUm2ZREO/NuAQDj4cZZkfQMeEW6rhqeKNUosswl0c68WwDA+GUzKzoH6RlwP/n6mGVXDWNTY0fSl9PVJFdc2trE5Zeb3+W6TegAMDY5Kzr7xkN6BlxNz5amvRlu6Eann7BteVKgUoJBcfhw2soYuQ792GOq/ysAIF/0k1z1WTGRsHM8OSI9A66l7w40CQYdXqphecK27MyvMn0DjWWGfvDBkfZ2ZGgAHpF5W6HCSM+AC+nx0vIAlLY2x75ipmniP/8z7QnbjpD5btHeToYG4C2yJNpRSM+A21juDnT8ASj6E4LPf97ivXLno4Nk3oQuM3RqbxQAgAJK7B4AgLyRCTO1/bzcHejg9eaWlrSLzaGQWLnSqeXbMkOvXGn9D5SVN87+5gGAC7H2DLjBmLsDHZm+jPXNJn7/yKaTcZywrZoxm6GyDg0AJrbOiqRnwPHS7Q50diPnbHKzI58TpGFshppKfo/J0AAg2Torkp4BB8u8O9DZ8dKyAEXueYzFbBhP0ZChASAzvcmSTbMi6RlwKsslZ8fvDtR1do7+Wc/Nzc1OfkKQC5mhLZ8AkaEBwEifFYvVrYj0DDhPhiXnWMz5uVnn93sxNxvJGpUM69D0tgPgQRl2iRRlViQ9Aw6TriGdHLDoUQAAIABJREFUbCLs9B10SeQZ197MzUYZajnoDw3Ag/RX51IVZVYkPQOOIZecw2GLJee2NusD7BzP47nZaMwMHY2SoQF4SCg0xqz4xBMFmhVJz4AzyKkgXZUzIdMrMmToSGQkQwOAd2SYFb/5zQLNiqRnQHVyybmhwXw9GHRyQzpMROYM7fNZdCwBABcbc1bMK9IzoDTLrsf6VjonLTmT5/Iuwxkr4TDr0AA8J92smEjk9/OQngFFySVnN5yBIrtDhMN5f/aPTOcUahq1HAA8J/PprXlCegZUlGHJ2UlnoGjayCIonYkLKpsMzdo/AO8wzor5XngWpGdANTJwpqYgh52BorekNoU2lp8LJ3OG5mkMAK+Rs2IBkJ4BhVgGTrnk7LzcnJrh5L8EBaVn6NTW37KEprGRxnYAMBEldg8AgBBCaJpoabFecnZSbn7pJRGPW4Qzv1+EQs75lzif7AEu47Lp2/GLX4w8t2lqsmdsAOBwpGfAfpa7A50VOEt27740HBZdXeZ3OOuf4TJ+v+jsFO3tFkfsRCJlmzcP33GHWL/enrEBgGNRuQHYKV1jDSdVOWuaaGgoueGGElN01vvqOeOf4V7BoGUxdElX19QNG2jKAQC5Ij0DtmlvFw0N1o01nBE49RLn1L1oel89x/QHcbt0RwnoTTnYUAgA2SE9AzbQjw9MeTndOUvOIs0uQFlx66S+el6SoSlHQ4P47GfZUAgAYyI9A8Umg4qDl5zTkbnZstsD1JGhKcfOnRRyAMCYSM9A8eiVDqYFvmDQseXBsgu93z/44IPvvPYaudkx/P7el1/ufflli5cIOKEQADIiPQNFkmHJua3NyWUO8h9AI2cnSrOhkGJoAMiA9AwUXLol57/+a8cuORuxNdDpMmwobGiwKM8HAG8jPQOFZXnytlxyfvttYieUIYuhQyHz9fZ2CjkAwIj0DBSQZT83ubnO8UvOcB+/X8Ri1hsKKYYGgPNIz0BBaJp47DHrJefOTpacoTD59I5iaABIg/QM5J+sF33wwaSLcl1P6SVnWaDt89k9DiggczE0i9AAPIz0DORTug2CcslZ6X5ulj1B4HHpOkNTyAHAw0jPQN449RiU1MjP8jN0spAjtasihRwAvIr0DOSHI49B0XMzS87ILENnaNnVDgA8Q8X0/P7772/YsOG6666bM2dObW3trbfe+pvf/CYhjzQ7r7u7+957762trZ0zZ87ChQu3bNkyNDRk14DhcTKCOu8YlHSlGnKtEUglCzlSf2boagfAS5RLz93d3cuXL3/uuecuvvjiW265Zf78+fv377/zzjt37NihP+att95atmzZjh075s+fv2zZsuHh4Ugk0tzcTIBG8aWr1nDGkrNpqVzvCaJ0gTZs5fePZOi/+Zuk6xRyAPCMErsHkCSRSLz44otHjx795je/uWrVqkmTJgkh9u3bt3r16kceeeTqq6+eNWvW0NDQs88+29fX98wzzyxZskQI0d/ff88992zfvn3JkiWLFi2y+x8Br9A00dJisQyndJVzukELISIRsXKlwkvlUInfL37xC4vXXOSzyVBIxGL2DAwACk+ttec///nPr7766hVXXHHzzTfL6CyEuOaaa2666abu7u63335bCHH06NGOjo76+vrg+eWx8vLypqamKVOmvPLKK6YCD6BAMpwgqHR0Th20MCyVE52Rk3SFHPG4CAREPF78EQFAESiXni+44IIrrrhi2rRpxuuXXHKJ/udDhw6dPHny2muvLS0t1S8GAoGampqDBw+eOnWqeMOFV8kiT9ML1EpvENRLNVKPPaRUAxOhF3KYfoTkUzUKOQC4kVrp+corr9y5c+emTZtKSkZLSvr7+9va2srLyz/60Y8KIXp6eoQQtbW1xr84ZcqUysrKvr6+gYGBIo8ZniJTqKnBgAM2CMohmshBK5r34SgZjifkaBUArqNWek6VSCS2bt164MCB66+/XibmY8eOpT7soosuqqqqGhgY6OvrK/oY4RWO3CBoiVINFEK6Qg52EwJwF7V2DZokEonW1tbvfve7c+bMeeihhyZPniyEsGys4fP5LrhgjGcCra2tra2tlu9at27dvHnzJj5g5NF777334Ycf6uXvttu4cdqTT5aZLjY19d5/f78Q4p137BhTTv74x1mXXTZcUzOwfHn//fcLkedBnzlz5i9/+UsePyAKra+vz+fz9ff35/ODTpokvvrVks9+dsYtt5R0dY1e1zTR0DC8cOF7P/pRPj+dx6g2KyIzZkU1vfHGG4899pjlu7q6upqamrL5IOqm5w8//PDFF198/PHHL7vssu9///szZ86U12WGNkkkEufOncv8ARcsWLB8+XLLd1VVVc2YMWOCA0Z+nTlzZvr06cYaHrtomti+XTz55FTjRb9fhELiwQenCjE13V9UTigkvvWtqTU1hRjx4OCgEILfIweRc2llZWX+P/SMGcN/+EPJhg2mdeiS3btnXXbZ4IMPcjrP+KgzKyIbzIpqamxsnD59uuW70q2xprLtl3DXrl2rVq0yXnn++ecbGxvlnwcGBqLR6Pbt2z/5yU9+73vfq66u1h82e/bs1I92+vTpnp6esrKyioqKdJ+xpqamvr4+T8NHwV144YVTp061/T6haWLJEou2yOernJ0TnYUQsVhJIX/n5besYB8eeSa/WQX8ljU3i5UrRThsqtmYumGD+PGPRSzGXtVcKTIrInvMimpKlwb37NmT5UdQse75xIkTd911V2tr6+c+97mXXnrJGJ3F+fR8+PBh48WzZ8/29vZWVFSUlZlfWwfGzfJEEdmjgoJhYGzyiWZq72d2EwJwMtvSc2Nj49FkcuG5v7///vvv37t371133fX000+bWtcJIebOnTt9+vSOjo4PPvhAv3jkyBFN06666qrUxwPjkO7w7VjMaRsEAduFQuwmBOAmaq09Dw0NPfroo7/61a8eeOCBBx980LLEuaampq6urqOjY9euXfJslP7+/k2bNp07d27p0qU+n6/oo4bbZOitEQrZMiLA4fS20KZXbeQvWzhsz6gAYFzUSs+//e1vf/KTnwghWlpaGhoark+2e/duIURpaemaNWvKy8vXrl17xx13PPDAAzfccMPu3buXLVtGWTMmjmoNoFD8fs4mBOACaqXnvXv3DgwMJBKJ48ePd6WQ21eFEHV1ddu2bVu8ePH+/fu3b99eUlISiUSi0ajlWjWQpXTVGioevi3HyistcKIMZxM2NJifuQKAetTaurt69erVq1dn88hAILB58+ZCjwfeIV9ATt9bQyWWYwUcRP5qpT5bbW8XgYCST1gBYJRaa8+ALRxTrSGXnI1jZfkZzmW5CC2EiER4fghAZaRneJrDqjUsNzPS9gvOJReh29rM1+UiND/bAJREeoZ3ZeitoVZ0Tl1ylmihB3cIBjO1tGMRGoBiSM/wKCdVa1hmfDlWTmuDO8iWdqn7DDSNRWgAqiE9w3McU62RYclZueVxIB8yLELPmcMiNABFqNVzAyg0x/TWSDfQUIjcDJdrbhYrV5p//js7accBQBGsPcNDLBOpctUaLDkD6c5V4XBvAAogPcMrUhOpotUaGaqcFcr4QOFlONybSmgA9iE9w/3SFTqruJLr97PkDIzKvAhNJTQAO5Ce4XKWi7lyb5LqK7ksOQNSukVo2nEAsAPpGW6Wrloj9XAGhSQSQrDkDCRjERqAMkjPcKd01RrNzU5IpIkES86ABRahASiA9AwXylDoHArZMiIAeZJhEbqhwYbxAPAe0jPcRhY6x+NJF6kfBlzFchG6vZ1+dgCKgPQMV3FGWzoAE2e5CC2fPbMIDaCQSM9wCSe1pQOQL83NFruAWYQGUEikZ7hBujNGlDt/G0DeyQ6UwWDSRTkpPP+8PUMC4GqkZzie6udvy1VxAIUjnyunLkJ/7WssQgPIO9IznE31Qmd9Vdzns3sogNtlWITmGSyA/CE9w6k0TfzgBwoXOmuaiMeToj0BGig0OQWk62fHoSoA8oH0DEeS1RBf/3rSRYUKneVyVzicdNHvZwEMKAbZz860CN3eLhoaqOIAMHGkZziP6h2dU6tJhFKr4oAHWC5C088OQD6QnuEwpmoIoVShc7q2eQpFe8BLZD87DlUBkFcldg8AyEG6js5K5FLL3h8KjQ/wJLmVMBxOerlK386rxNNuAA7D2jOcIcNhKPZHUzm41GoNlpwBRcRiFv3s2EoIYFxIz3AAy8NQVImm6U5qYVkLUIplPzu2EgLIHekZqtM0hQudLZecg0E2CAIqyrCV0NQhBwDSIz1DaTKdGvn9orlZmWhqueSsRDUJgDRkPzvTL6ncj8wiNIAskJ6hqK6ukkjEutA5FLJlRFYSidE/05MOcAq/X3R2mqcSTiUEkB3SM1SkaWLjxmkPP5zUE+Yf/1GNQmcTGaBVqcIGkLV0WwmXLLFjNAAcg/QM5cgFoB//eKrxYiQiHn7YrhGNRZUqbAA5stxKuGMHVRwAMiA9Qy1K7xFMR+nBAcgow1ZCqjgAWCE9QyGWewSpJQZQcPJUQhPZEBoAkpGeoQSlD0MB4AXpGkJTxQEgGekZ9rOMzsuXD/zhD8NEZwDFQxUHgCyQnmEzeWOKx5MuRiLiqadO2TMgAB5n2RA6EhFz53KsNwBBeoa9ZHR22B5BAK4nF6FNVRxHjnCsNwBBeoaNUk+5VmKPoCxzBOBxVHEASIP0DHsoukcwGh1ZDPf5bB0HADWkq+KgFwfgYaRnFJvlHkG52d3O6CyXlEzDAgB5rDe9OACcR3pGUVlm1EjEotFqUclhmW6EvDgLQNfWJmKxpCtUcQBeRXpG8ai4R1CuhDvveEMARRcKUcUBQJCeUTSWR3CHQnZH55YW6/projOAVJa9OKjiADyG9IxiUPEIbssiEvvrrwGojV4cgOeRnlFwKrbXSFetYXP9NQCHoBcH4GGkZxSQZXsNy9LB4rEck98vYjGqNQDkQC4DfOELSRep4gA8gPSMQrGMqZGIedt6UVlWa1gWMgLAmPx+8ZOfWFdxxOO2jAhAEZCeURCptw/7+1ikVmsIISIRCp0BTEhzs0XRVzgswmE7RgOg4EjPyD/LznQ2t9cQwvzp7Y/zANxCbjg2vYQVj1s8YwfgfKRn5Fnq/cL+9hqpVBwTACfL0IuDMmjAXUjPyKdo1Pxapf3tNYwSCSGo1gBQMKlVHDSzA1yH9Iy8Sd0jqGL35ESCJWcABWRZxUEzO8BFSM/Ig3TtNeieDMCL5Ituy5YlXaSZHeAWpGdMVLrozAovAE9rbaUMGnAl0jMmRMXOdACgCMtmdpRBAw5Hesb4KdqZDgDUQRk04DqkZ4yTpjmhMx0A2E5OjqFQ0kXKoAHHIj1jPGRTZyO1OtMBgGpiMRGLJV2hDBpwJtIzcqZWU2e5Bg4A6guFKIMGXID0jNykttf4X//LvqbO8qVPTRM+nx2fHgByRBk04HykZ2QrXWe673zHvtEY7zcEaACOQBk04HCkZ2RF00RLizJNnWWxoGk0plsRAKiMMmjAsUjPGFtqWLWzqbNln7xIxHwfAgDFUQYNOBPpGWNQq6lzNGrRJ48W0wAcijJowIFK7B4AlGYZnWMx81RfpKGk1o7QJw+A08l5zFSzIcugOzttGxWA9Fh7RlrpzkOxJzqn7liUazZEZwAu0NZmnuLkFEwZNKAe0jOsqXUeSkODiMeTrkQiFvWCAOBczc3mxWb58p9p9gNgN9IzLFieh2LPOm97u/D5LPYIUugMwH3kVGt6gS8cZh8hoBTSM8xSSyRCIZuq71K3zsgFcKIzALeyrJBjHyGgEtIzklieh2JXL7iShx9Oeps9ggA8IrUMur390s98pmT3bnvGA8CA9IwR6Y4StHGdd3hoKGko7BEE4B3Nzaali5KuLhEOs48QsB3pGUKodpSgUSKhzFAAoLhSj1NhHyGgAPo9Q2iaeTlDrRNIZIAGAA+SrTlNc3Q4LF59lQNWAbuw9ux1ciFD3egMAB4nt3zceWfSxXicfYSAXUjPnpbuKEGiMwCopaVl4P77k67I8wiNMziAoiA9e5dldLbnKEEAwFhONTUN79yZdCn11UMAhUd69qh00ZmeFgCgrmDQeh8hARooItKzF2ma+eU+ojMAOIPcR2h6lZBGHEARkZ49Jx4XgUDSFdtO4QYAjINlmV04zD5CoDhIz94Sj4twOOmKjM4AAIexOo+QAA0UAenZQ6JRc3QOhYoeneWRhj5fcT8rALhRynmEI404KIMGCon07BWWp3AXu9e+3N0ix0GABoCJszyPkAO9gUIiPXuCZXQudlPn1DYfpvprAMA4yH2Exs0rHOgNFBLp2f1Uic6pbT44lAUA8iLdPsJo1J7xAK6menr+j//4j4997GM/+MEPTNe7u7vvvffe2traOXPmLFy4cMuWLUNDQ7aMUGWyxtj+6ByNWrT5aGsToVBxxwEA7mUZoCMR9hECead0eu7s7NywYUNqLH7rrbeWLVu2Y8eO+fPnL1u2bHh4OBKJNDc3E6CNNE20tCRFZ7/fpuhsyu80lwaAAqERB1B4I+n5gw8++O///m+l0ucHH3zw6KOPvvvuu6brQ0NDzz77bF9f3zPPPPOjH/3oiSee2Llz58KFC7dv397R0WHLUBVkGZ1DoeJGZ8ulb9nmg+gMAAVCIw6gwEbSc39//9133z1//vxvfvObr7/++ocffmjvsIQQ27dv371795e//GXT9aNHj3Z0dNTX1wfPvz5VXl7e1NQ0ZcqUV155JZFIFHug6pH7rVWMzja0+QAA76ERB1BII+l56tSpn/zkJ4eGhlpbW5cvX/6pT33qO9/5Tmdnp11h9M0333z66aeXLVvW2NhoetehQ4dOnjx57bXXlpaW6hcDgUBNTc3BgwdPnTpV3JEqJ3WG9PtFLFb06Gza7m1P1QgAeFW6RhwEaGDCRtLzxRdfvGnTpt/97nctLS1/8zd/c/bs2Xg8/rd/+7ef/vSnn3zyya6urmLG6P7+/scee+ySSy5Zs2bN5MmTTe/t6ekRQtTW1hovTpkypbKysq+vb2BgoGjjVFDq3Cijs2kbSTEGYWqvUeylbwDwPMt9hHSyAyYsadfg5MmTFy1atHnzZhmjv/CFL/T29n7ve9+7/vrrGxsbX3jhhRMnThR6QIlEYuvWrf/1X//1rW99q7q6OvUBx44dS7140UUXVVVVDQwM9PX1FXqEyrJMrakzZ2HJ6rrUQRCdAaD40nWyMx08CyAXJZZXZYxetGjR0NDQm2+++a//+q9tbW2PPvro+vXrL7/88lWrVn3uc58rKysrxIDeeOONF154YcWKFQsXLrR8gOXWRp/Pd8EFY/QPybCn8MYbb6yqqsppnKrp6ir5u78rM6bWmprhl18eqKwUvb3FG0Zl8s7u4ZqagZdfFuMaRF9fX2lpaUmJ9Y8oVDM4ONjX11deXm73QJCt3mJODciH8c+KL79cctddZa2to1ficaFpvS+/nMfhwYRZUU09PT0/+9nPLN8lt9Vl80HGSJzHjx/fu3fv66+/LledE4nE4cOH161b9+lPf/qFF17Ie4+O/v7+9evXz5gx4+tf/7ovzUnOqbUccmDnzp3L72AcRNPEkiVTTQu+//mfg8XvbNFrrDv3+wd+97txt9fw+XzsAXWWdL+zAPJiIrPi8ObNqZ3spi5ZMvFRIQNmRbeyeAqbSCS6u7t//OMfv/zyy7JhnM/nu/rqq1euXHnDDTcIIX72s5899dRT69evP3369De+8Y3xfeJdu3atWrXKeOX5559/44033nrrrRdeeGHGjBnp/uLs2bNTL54+fbqnp6esrKyioiLdX6yvr29qahrfaFWmaeLLXxZdXaNXzvdTLsiLA2NLJITPJ/cIVk7gw/T390+bNo21Z6cYHBwcGhqqrJzI9xw24FvmIBOdFZubxeLFxt7PUzs6pn7qUzTgLxBmRTVVVlaa9s6Nw+gvYSKR0DRt27ZtL7/88vHjx+XFQCCwYsWKm2++edq0afojb7755lmzZt19990///nPx52eU505c2bfvn0DAwO33Xab6V2PPfbYY489tm7dutWrV8v0fPjwYWM7jrNnz/b29lZUVBSonkRZ6WqdbZ4Jaa8BAAoKBkVbW9LhKfIuUuzd5YCzjaTnEydOrFy58ve//718s7q6+vbbb//iF784c+ZMy78WCASmTZt25syZcX/ixsbGo0ePGq+cOXPm3Xff9Sfnvu7u7l/+8pfz5s278sorP/axjwkh5s6dO3369I6OjpUrV+pN644cOaJp2he+8AVjync9RaOzEERnAFCU7GRnvHnIe0mx95gDDjaSnhOJxOnTpy+55JIvf/nLd95558yZMzMX6wwNDd122211dXV5HMqFF1549913my7u2rXrl7/85Y033rh69Wp5paampq6u7rXXXtu1a9dNN93k8/n6+/s3bdp07ty5pUuXeqfGSN3oDABQmbxbmI4GkCvQoZBdgwIcZCQ9l5eX//M///Oll146adKkbP7azJkz9ThbZKWlpWvWrHn99dfXrl27devW6urq3bt3Hz9+fMWKFVnulHQBTROBQNIVv190dto0GgCAs8gAbTogIBwWx47x4iEwppGeG6WlpTU1NVlGZ9vV1dVt27Zt8eLF+/fv3759e0lJSSQSiUajlu043IfoDADIg9RqjUiEVtDAmFRvaJBaHi0FAoHNmzcXfzy2IzoDAPKmrU1Eo0nN7OJxoWmirc22IQHKG6PfM5SSGp1XrSI6AwAmoLlZxGJJV9rbRfLRVwCMSM+OkRqdQyHx3HM2jQYA4BqhkHmxub3dfMsBcB7p2Rkso7NpsaCwnz4aLdYnAwAUnWwFbSRvPMZthQCEEKRnR4jH7Y7O4bCIRIRnugECgBfJVtBGcv4nQAPJSM+qi8fNG6CLHZ2NLY0I0ADgYnIfurERh+kuAID0rDglorPpRBbmUABwMb/f4uDuhgYRj9syHEBBpGd1qRidOcoVAFzPcrYPh9kAA0ikZ0WlRudIpLjRORDgHHAA8K62NvPB3ZylAgghSM9qsozOxTs8NXWXItEZADwoFks6SEUIEY+L22+3ZzCAMkjPykmNzi+9VMToHI2aP73chU10BgAPSj1LZetWzlKBx5Ge1WK56ly8F8pM57UKqxb6AABPsTxLhQANDyM9K8TOgg15HoopOhe11BoAoKrUs1Q4jBAeRnpWhc3RuaXFIjoXr14EAKA2DiMEziM9K0Gt6Oz3E50BAGYcRggIIUjPKrC5w4bMysY3QyGiMwDAguVhhARoeAzp2WY2R2cpkRj5g98vmpuJzgCAtFIPI+Q0b3gM6dlOSkRnKZEYmRBNvfEBADCxPIyQAA3PID3bRqHoLJlejAMAIAPLAB2P2zIWoJhIz/aQdWJG7NMDADhMaoAOhwnQcD3Ssw1kkx8j9ukBAByprc3c8DQcFtGoPYMBioL0XGyW0ZkzSQAATtXcbHFiQPGOyQWKjfRcVERnAIALNTebb2bxOKd5w61Iz8VDdAYAuFbqLa29nQANVyI9FwnRGQDgcqGQ+TRvAjTciPRcDERnAIAnBIMEaLge6bng5BlMRsWLzux6BgAUmWWANq0hAU5Gei4sGZ01bfRKUaNzJCJ8vqJ8MgAAzksN0KkvwgKORXouoNToLA/DLsYnltFZIkADAIosGBSdnUlXCNBwC9JzoVhGZ9NMUqhP3NKS1HrT76eEAwBQbPK25/ePXpEBur3drhEBeUF6Lgg7o/M//7M5OnOSIQDAFn6/+TRvTRPhMAEajkZ6zj87o3M4LL797aRPTHQGANhI1iwSoOEipOc8s4zOpr0ThfrEpslITlhEZwCAvQjQcBfScz7J2SA1OhuLvgr4iVOjs3GqAgDALpYlHA0NBGg4Eek5bywTbJGis2kCSp2kAACwXeq9yfRyLeAEpOf8sDk627DcDQBA7lIDNF044DSk5zyQ7ZWJzgAAjM1yBZoADecgPU+UbK8cj49eIToDAJBJW5tYsybpCgEazkF6nqjUk0mKlGCJzgAA5/re91iBhkORnifEeB62ON/ookgJ1thBmugMAHCctjYRCiVdIUDDCUjP42cZnYva6CKRGPnERGcAgBPFYhYB2lgNCainxO4BOFVqdG5utqNHXCIhNI3oDABwqlhMCJGUmMNhIYQ5VQPKYO15PFKjcyhk36850RkA4GipK9DhMCvQUBbpOWfxeFJ0FkKEQpyHDQDABBCg4Ryk59zE4yMvKOkiEaIzAAATFouNVHHoCNBQEuk5B+3tRGcAAAomFCJAQ32k52zJw0mMiM4AAOQZARrKIz1nRdNEIJB0hegMAEBBEKChNtLz2FJXndkmCABAARGgoTDS8xhkdDYeiZ36Gw0AAPLMMkBHozaNBhhFes4kNTrLAwUL/ll9vgJ/DgAAlJcaoCMR8/59oOhIz2lZRufOzsJ/VllhTYAGACA1QMfjrEDDXqRna5omwmH7orNEgAYAgBVoKIb0bEFG5/b20St+v2hrK/xnNfX1sO3sbwAAVMIKNFRCejbTNNHSYhGd/f4Cf9bU6MzmRAAAJMsVaLpwwA6kZ7OWFhGJjL5JdAYAQAm0sYMaSM9JolFzdI7FiM4AAKiBAA0FkJ5HWUbnYLCQn5LoDABATgjQsBvpeUQ8bo7OoRDRGQAA9RCgYSvSsxBCxOPm1jcFP4vb8vhvojMAANkgQMM+pOeR/nRGkUhRonOxzzAEAMBFCNCwidfTc2r1hD3RueAHsQAA4DoEaNjB0+nZsnqisNFZCKIzAAB5Q4BG0Xk3PacuARep8NiYlYnOAABMUChkPhDYdGIwkFceTc+y1tm2wuNEYuRTEp0BAJi4YNB8F29oIECjQLyYnmV0Np3FXewcm0gQnQEAyJtQKKn1rCBAo1A8l541TbS0mKOz6QUfAADgPM3NIhRKukKARgF4Lj23tJhPRWlrK/DSH1kpAAAgAElEQVRZ3AAAoDhiMQI0Cs1b6dnyLG6iMwAA7kGARoGV2D2A4onHxYEDo2/K6FzYs7gBAEDxyR2Exr51DQ2is5MFM+SFh9aeDxxo0v/s94tQiOgMAIBLpa6QBQKsQCMvPJSejYpxKgoAALBRW5s5QFPCgXzwYnou+FncAABABW1tIhxOusJBKpgwD6XnqVM7BKvOAAB4yksvJa1Apx76AOTIQ+l5/fo9sVghDxTUtKQNCgAAQAWmEg4CNCbGQ+lZCHMHm3ySp7CEwyIQKNjnAAAA42IZoIFx8VZ6LiD9FBZNI0ADAKCc1ADN/RrjQnrOB9MpLELwehAAAMohQCMfSM8TZnmAIa2kAQBQkOkerWmiocG2wcCZSM8TkxqdOYUFAABlpS5ytbcToJET0vMEWEZn+uEBAKAyGaCNCNDIBel5vOJxc60z0RkAAEfw+0VnZ9IVAjSyRnoel3jc3OmGAwwBAHAQAjTGi/Scu/Z2ojMAAI7n94u2tqQrqbd4IAXpOUepm3OJzgAAOFQwaA7Q8biIRm0aDZxBxfT84Ycf/vSnP/3sZz97+eWXX3HFFV/5yld+85vfJBIJ42O6u7vvvffe2traOXPmLFy4cMuWLUNDQwUfWWpjSKIzAACOlhqgIxERj9szGDiBcul5aGhow4YNf//3f9/T0/P5z3++oaHhd7/73Z133rljxw79MW+99dayZct27Ngxf/78ZcuWDQ8PRyKR5ubmwgbo1FXnhx4iOgMA4HipATocJkAjnRK7B2DW0dGxZcuWz3zmM88888y0adOEEAcOHLj77rs3bdq0YMGCj3zkI0NDQ88++2xfX98zzzyzZMkSIUR/f/8999yzffv2JUuWLFq0qFAja2gQmjb6ZigkHn20UJ8LAAAUkwzQxmWycFj4/ZzhgFRqrT2fOXOmpaWlvLz829/+tozOQoh58+YFg8E//elP77zzjhDi6NGjHR0d9fX1wfM/0OXl5U1NTVOmTHnllVdMBR75ZNyZm9oqEgAAOFowaL65NzSI9nZ7BgOFqbX2fPLkybfffnvBggWXX365ftHn8z3++OP6m4cOHTp58uS1115bWlqqXwwEAjU1NQcPHjx16tRHPvKRQo0vkRA+n0WPGwAA4AKhkDh2LOk8h4YG0dbGCjSM1Fp7PnHiRF9fX21t7TvvvHPXXXfV1tam7hrs6ekRQtTW1hr/4pQpUyorK/v6+gYGBgo7xESC6AwAgGs1N5tPQ2MFGsmUS88DAwNvvPHGLbfc8vvf//6mm2667rrrDhw4YNw1eOzYsdS/eNFFF1VVVQ0MDPT19RV3yAAAwF2am0UolHQlHCZAQ6dW5Yb0i1/8YsWKFdFodPLkyUKIffv2rV69+pFHHrn66qtnzZpl2VjD5/NdcMEYzwS6urq6uros31VVVTXxYSO/Pvzww+HhYbtHgWwNn2f3QJCt4eHhRCLBt8xBmBWL6oUXSjRtNDFrmgiHh3fuFH5/lh+AWVFNsoRhglRMz3/913993333yegshLjmmmtuvfXW73//+/v27Zs1a5Z+3SiRSJw7dy7zh92zZ8/tt99u+a5169bNmzdvgsNGfh0/flwIMWnSJLsHgqycOXPm1KlTJSUqTimw1NfX5/P5BgcH7R4IssWsWGxbtsy45ZapHR0jb2qaaGh479e/zvJvMyuq6U9/+tPatWst39XV1dXU1JTNB7Htm7pr165Vq1YZrzz//POTJk3y+Xw1NTUXX3yx8V11dXXi/NOF2bNnp36006dP9/T0lJWVVVRUpPuMy5cvz/KLAkVceumlzDtOMTg4eOGFF86aNcvugSBb5eXlQojKykq7B4IcMCsW2//7f8ai55KurlnXX5/l9idmRTXNmjXrtddes3zXxo0bs/wgatU9f/SjH62srDx79qzplQ5jtYZMz4cPHzY+4OzZs729vRUVFWVlZcUZKgAAcD9Tw43Uo9PgPbal58bGxqPJGhsbZ86cedlllx06dMhYoJxIJPbs2ePz+ebOnSuEmDt37vTp0zs6Oj744AP9MUeOHNE07aqrrtK7RAMAAORBLJYUoNvbCdAep9bac0VFxY033njy5MnnnntO7z23f//+n/70px/72MdkaXJNTU1dXV1HR8euXbtkG7v+/v5NmzadO3du6dKlPp/Pzn8AAABwmdQj0trbxZe+ZNNoYD/lyqfuuOOON99889/+7d9+/etfL1y48N133927d+/UqVPXrl07Y8YMIURpaemaNWtef/31tWvXbt26tbq6evfu3cePH1+xYkV9fb3dwwcAAK4jD0oLBEav/Pu/i3CYg4e9Sa21ZyFEeXn5448/3tzcXFpa+vLLL+/fv3/x4sWtra2NjY36Y+rq6rZt27Z48eL9+/dv3769pKQkEonoHe7GQ9MEi9YAACAdv1+0tSVdicdFNGrTaGAn5daehRClpaUrV65cuXJlhscEAoHNmzfn5/PpOwB8PnH+REMAAIAkwaB5BToSEbNnm49Wgdspt/ZcbDI6a9rIm6xAAwCAdFJXoDmG0Hu8nZ5N0VmIpE21AAAAJsGgudzZ0BMaXuDh9KxpIhxOis6pTygBAABMQiERiSRdIUB7iVfTs6aJaDTpB53oDAAAstTcbC53poTDM7yanltaRDw++qaMzn6/XcMBAAAOYzpFRb6mDQ/wZHqORpNecCE6AwCAcUg9x9vYkQMu5b30nBqdYzGiMwAAGI/UAM053m7nsfQcj1tEZ/psAACAcTNlifZ2ArS7eSk9x+PmgqRQiOgMAAAmRC7GGbW3l9xwg02jQcF5KD03HTiQ9HYkIpqbbRoLAABwEb9fdHYaL5Ts3j1t40a7hoOC8lB6TkJ0BgAAeZTS+rbsySeTGnzBLTyZnkMhojMAAMizYJBzvL3AQ+m5Y+pUIYQIhczFSQAAAHnBOd4e4KH0vGf9eqIzAAAoLM7xdjsPpWchBNEZAAAUnOU53ppmy1iQdx5LzwAAAIU3+Oyzg/X1o29zioqLkJ4BAADy78S2bRxD6EqkZwAAgMIwnePNMYSuQHoGAAAomFhM+P2jb7a3m08+htOQngEAAAom5RQVEY+LaNSm0SAPSM8AAACFlBqgIxF62DkX6RkAAKDAUo8hpAm0Y5GeAQAACo9jCN2C9AwAAFAUoRCnqLgA6RkAAKBYYjGaQDsd6RkAAKCITE2gNU0sWWLbYJA70jMAAEBxmQL0jh2sQDsI6RkAAKDoTDsI29tpAu0UpGcAAICi8/tFZ2fSlUhExOP2DAa5ID0DAADYIfUUlXCYHnbqIz0DAADYhFNUHIj0DAAAYJ9gUEQiSVdYgVYb6RkAAMBWzc3mHnbhsG2DwVhIzwAAAHZLbQJNDztVkZ4BAAAUYArQ7e0EaDWRngEAANQQiwm/f/RNmkArifQMAACghtQedjSBVg/pGQAAQBk0gVYe6RkAAEAlwaD5GEKaQKuE9AwAAKAYv9+iCTTUQHoGAABQT2oTaFpwqIH0DAAAoCR62CmJ9AwAAKCq1ABNCYfdSM8AAAAKi8WS3ozH6WFnL9IzAACAwuhhpxjSMwAAgNqCQXOApoedfUjPAAAAygsGLXrYaZotY/E40jMAAIAT0MNODaRnAAAAh2hrEzfcMPomAdoOpGcAAADn+PnP6WFnL9IzAACAo9DDzlakZwAAAEehh52tSM8AAABOQw87+5CeAQAAHMiyhx0Kj/QMAADgTPSwswPpGQAAwLHa2swtOAjQBUZ6BgAAcLJYzBygKYAuJNIzAACAk/n95h527CAsJNIzAACAw6X2sCNAFwzpGQAAwPlSe9iFw0LT7BmMq5GeAQAAXCEYFKHQ6Ju04CgM0jMAAIBbmHYQEqALgPQMAADgIqk97KJR2wbjRqRnAAAAdzG14IhE2EGYR6RnAAAAd6EFRyGRngEAAFwntQUHATpPSM8AAABuFAyKSCTpSjhsz0jchfQMAADgUs3NtODIO9IzAACAe9GCI99IzwAAAK5GC468Ij0DAAC4Gi048or0DAAA4HapLTjCYaFp9gzG4UjPAAAAHmBqwaFptOAYH9IzAACAN5hacLS304JjHEjPAAAAnkELjgkjPQMAAHgJLTgmhvQMAADgJbTgmBjSMwAAgMcEg+YVaHYQZo30DAAA4D2hkAiFRt/kEO+skZ4BAAA8KRYTS5eOvkkLjuyQngEAALzq3/9d+P2jb7a3i3jcrrE4BekZAADAw1LPIGQHYUakZwAAAA+jBUeOSM8AAADeZjrEW9CCIxPSMwAAgOeZDvGmBUd6Kqbn999/f8OGDdddd92cOXM+8YlPNDU1dXd3mx7T3d1977331tbWzpkzZ+HChVu2bBkaGrJltAAAAG7AId7ZUS49nzhx4s4773zuuecuvvjiW2655aqrrvrJT37ypS996cCBA/pj3nrrrWXLlu3YsWP+/PnLli0bHh6ORCLNzc0EaAAAgPHjEO8sKJeeW1tbf/vb365YsWLHjh3r16/funXrU0899f7778diseHhYSHE0NDQs88+29fX98wzz/zoRz964okndu7cuXDhwu3bt3d0dNg9fAAAAMdiB2EWlEvPhw8fLisru/XWWydPniyE8Pl89fX1VVVVb7755qlTp4QQR48e7ejoqK+vD55/caG8vLypqWnKlCmvvPJKIpGwcfAAAADOxg7CsSiXnidPnnzmzJne3l79yuDg4PDw8MUXXzxlyhQhxKFDh06ePHnttdeWlpbqjwkEAjU1NQcPHpQJGwAAAOPEDsKMlEvPt95668UXX/yd73znzTffTCQSJ06c2LBhQ09Pz+c///mKigohRE9PjxCitrbW+LemTJlSWVnZ19c3MDBgz7gBAABcgx2E6SmXnuvq6rZs2SKEWLp06eWXX75gwYKOjo7HH3/8q1/9qnzAsWPHUv/WRRddVFVVNTAw0NfXV9ThAgAAuFIslnSINzsIzyuxewBmXV1dkUhE07RPfOITV111laZpe/fu3bBhQ1VV1Wc+8xkhhGVjDZ/Pd8EFYzwTaG1tbW1ttXzXunXr5s2bN/HBI4/ee++9Dz/8cNKkSXYPBFk5c+bMX/7yF7tHgRz09fX5fL7+/n67B4JsMSs6ixtmxUmTSh599NLbbhu90tBw4l/+ZXDBAvvGNFFvvPHGY489Zvmurq6upqambD6IWul5YGBg3bp1b7zxxtNPP33TTTf5fD4hxL59+1avXr1u3bof/vCHgUBA7iY0SSQS586dy/zBFyxYsHz5cst3VVVVzZgxY+LjRx6dOXNm+vTpJSVq/YgincHBQSEEv0cOIufSyspKuweCbDErOotLZsUvfWl4586SG27QL0y7777hP/zBxhFNUGNj4/Tp0y3flW6NNZVtv4S7du1atWqV8crzzz9fUVFx4MCBxsbGJUuWyOgshLjmmmvuvffeSCTy61//OhAIzJ49O/WjnT59uqenp6ysTNZGW6qpqamvr8/vvwKFc+GFF06dOpX7hIPIb5ndo0C25DeLb5mDMCs6jktmxcZGEQqJeFy+VdLVVbJkibmrnaOkS4N79uzJ8iOoVffc19c3ODiYOjtUV1cLIeQrjDI9Hz582PiAs2fP9vb2VlRUlJWVFXG8AAAAbheLsYPQyLb03NjYeDRZY2NjRUXF1KlT//znP3/wwQfGB7/77rvi/OuMc+fOnT59ekdHh/ExR44c0TTtqquumjZtWpH/IQAAAC7HDkIDtdaea2trr7zyyo6Ojl27dunnnvzhD39oaWmZMWPGokWLhBA1NTV1dXXGx/T392/atOncuXNLly7V6z0AAACQH36/+RBvD59BqFb5VHl5+T/90z+tWrXqG9/4xqZNm+bPn9/d3b13714hxD/+4z9eccUVQojS0tI1a9a8/vrra9eu3bp1a3V19e7du48fP75ixQrKmgEAAAoiGBRtbUnHpoTDorPTvgHZRq21ZyHEvHnztm/f/pWvfOXEiRPbtm3bu3fvwoULf/zjH9955536unJdXd22bdsWL168f//+7du3l5SURCKRaDRq2Y4DAAAAeWA6xNurZxCqtfYszZw5c/369evXr8/wmEAgsHnz5qINCQAAAKK5WbS3j9ZsyB2Ezc12DqnolFt7BgAAgLra2jy+g5D0DAAAgFx4ewch6RkAAAC5kDsIjcJhm4ZiA9IzAAAAchQMilBo9E0v7SBUcdcgAABe0NHRkf3hwL29vZWVlQUdD/JoeHh4YGDA5d+yujph/AceOCDuuy+pJNpWCxYsKFAvY9IzAAD22LNnT0dHR5Y3eJfnMNcpKSnxxLfM2MBOJR0dHUII0jMAAG5TX1/f1NRk9ygA5IC6ZwAAACBbpGcAAAAgW6RnAAAAIFukZwAAUBA/+MEP5qT41Kc+9dBDD3V3d9s9OiUMDAzcfvvtt99++8DAwDj++vHjxxcvXvzAAw/kfWDIgF2DAACggBYtWjRz5kz9zYMHD/7Lv/zLvn374vG48XrRHD9+PBaL/d3f/d3HP/7x4n92uADpGcD/396dxjVxdQ0AnxiCRBIRBNlBggG0RhbLogaBigugIFYFt+JCqK2CgqhgVZZaqYBWFAXFBXfRKgpl01hEUSOgSMGdRUuCgWACJKwh5P0w75MnDyAGt6Ce/88P5s6dO2cmGk4uZ+4AAMBHtGTJEmdnZ8lLsVicmJgYExNz/vz5tWvXfvp4Ll68ePr0aVdX109/aPBlgMoNAAAAAHw6GAzG2dlZXV39/v37zc3N8g4HgH6D7BkAAAAAn5SKigoej+/s7BSLxQiCsFiskJAQGxsbEolkbGzs5OR0/PhxoVCI/KcseN26dUeOHDEzM6NQKGlpaWj7jh07rK2tSSQShUKJjIxsampCB6fT6SQSKT09fffu3WgHKpWalpYmEokQBAkODo6Ojubz+R4eHr1WG6O7p6WlRUZGmpmZGRsbe3p6FhYWSjqIRKKMjAw3NzczMzP06DQaraqqCt2amJjo4OBAp9OpVCqZTA4ODu7o6OjjBCUYDIarq6uxsbG1tfWOHTukA2ttbT127BiVSiWRSGZmZr6+vs+ePev1wvYdG/hQoHIDAAAAAJ9UeXk5h8OxsbFRVlauqalZsWJFfX39vHnzxo4d+/Lly5SUlIiIiMGDB3t5eaH96XT6P//8s3Xr1traWgqFwufzV61adevWLSqV6unpWVJScv78+fLy8n379hGJRHSXX3/9FY/Hr169GkGQI0eOrF+/HofDubi4LFq0qKurKzs7OyAgwMLCQklJqdcIt23bhsfjQ0NDEQQ5ePDgkiVL4uPj0fqTI0eOxMTE2NjYoEHS6fScnJxXr16dOHFCVVUVQZDa2tpNmzbNnTtXU1NTQ0Ojvr7+rSf48OHDdevWOTs7+/n55ebmHjx4sKKiIi4uDo/H8/n8gICAGzduUKnU4OBgJpOZnJw8b968PXv2ODg4dAv7rbGBDwKyZwAAAGAAWbZM3hG8Kx8fxNHxLX1EIlFZWVlkZGRXV5e7uzsGgykqKqqtrd29e7ckF5wyZcrixYsLCwslyWVbW9vmzZslHY4fP56fn79+/fqVK1diMJjZs2fb2NgEBgYePnxYUkhNIpGSkpLQZNrOzm7x4sXXrl1zcXGxtLS8e/futWvXJk2aRKFQ3hSnioqK5KbGKVOm+Pj4JCQk2NradnZ25uXl2dvbx8fH4/F4BEE8PDwiIiJSU1OZTCaaoXZ0dLi6uq5fvx6DwSAIkpaW9tYTFAgEGzdupNFoGAzGw8PDzMxs9+7dBQUFDg4O169fv3HjRnBwMHqyCILMnj3bx8dnz549VlZW0jHzeLy3xgY+CMieAQAAgAEkOVneEbyrkSN7z579/Py6tWCx2MDAwAkTJiAI4u7u7u7uLr1VVVV1yJAh0i1aWlqjR49G/97c3Eyn07W1td3c3NBsEkEQe3t7KyurvLy8Zf/58kGlUiXz0BoaGhoaGnV1dc3NzcrKyrKcy5IlSyTrgejp6bm4uJw5c6a6unrMmDEnT56U7onBYLS0tLrtTqVSJbHJcoJkMtnT0xPdBa0LP3r0aHZ29qRJk3JycrS0tKRPFo3nyJEjT548MTQ0lB5WltjA+4PsGQAAAAAfkfSKdQoKCuPGjZswYUK3teoEAkF5efmLFy8KCwtv377NZDKtra0lW7W1tSXpZktLC4vFUlZWLioqKi0tlfTp6uqqr6+X3IaooPDfDEdRUXHYsGGSMmtZ6OjoSL/U1tbm8Xg1NTXoIncikYjNZj9+/LiysjI/P7+4uHjQoP/eSEYgEDQ0NLoN2PcJqqmpobPFKLQunMVi8Xg8LpdraGiopqYmPZqFhUVbW1tjY2PPyPuODXwQkD0DAAAA4CPqtmJdNzweb+vWrZmZmWKxGIvFGhgYWFpacrlc6T7S+Z9YLO7s7Kyqqur5iBAikfj69esPG7wEBoPBYrFisfjatWshISFohCoqKhQKxdzcXDqPx2Aw0gHLcoK9UlRUfFPi2+2OQ5QssYEPArJnAAAAYAAJD5d3BO+qxz1sbycWi/fu3Xv16tXIyEgPDw8CgYAgSF1d3b179960i7KysqGhoba29qFDh9D+3dTW1vY7jrcNUl5ePmzYME1NzefPn//yyy+jRo2KiooyMDDAYrEIgiQmJr4pQ5XxBBsaGjo6OiQvGxsbW1tb9fX1VVRU1NTUiouLuVyu9Mk+fPhQSUlJRUVFepD+xgbeGWTPAAAAwAASFibvCD6h5ubmJ0+eaGhoODk5odmhWCxmMBhsNruhoaG9vb3nLsrKylZWVomJiTdv3nRxcUEbWSzW0qVLhw8fnpCQ8NaD4nA4sVjc1dXVR5/09HR3d3e0cprJZN64cYNCoRgZGd26dYvD4SxZssTIyAjtyePxrl+//qY6ChlPsKKi4tatW7NmzUIQRCQSpaamNjY2Ojo6KigoTJ8+PSsrKyMjQ3LXIJPJzMrKIpFIo0aNkp6E/vfff/sVG3hnkD0DAAAAQD4IBIKNjQ2DwQgKCvL09EQQJCMj4+7du2KxuKWlpdf6BARBVqxYcf/+/YCAAHd3d0dHx+rq6pSUlNra2qCgIFlWljA0NBQIBCdOnOByuXZ2dtIFxxIFBQVeXl4+Pj4CgSAhIQGDwaxduxaPx5uamurq6iYlJTU1NZmbm5eVlaWmpvJ4PKFQ2NbW9s4nqKSkFBkZef/+fXNz89TU1Pz8fC8vr4kTJyII4ujoOHny5NjYWAaD4enpia5Y197eHh0draqqWldXJzlWf2MD7wyyZwAAAADIzY8//oggyKlTp0JDQ5WVlR0cHDIzMxMTExkMBo/H6zUbJhKJ8fHxCQkJly9fTk1NVVRUNDc3j4mJkb4Prw+2trazZ8++fPnynTt3zpw5Y2Bg0LPPqlWrmpubw8LCEAShUqkbNmwwMTFBEERfXz8hISEiIuLo0aNdXV0GBgaBgYEkEsnX17esrKzX8m5ZTvCbb75Zvnx5bGzssWPHRowYERYWtmDBAhwOh57s/v37z507l5SUFBQUpKioKB2PtHeIDbwbjOz3n37W4uLiEARZs2aNvAMBsqqurtbW1pa+aRoMZG1tbRwOR19fX96BAFk1NDQgCDJs2DB5B/JVg59NAxCdTvfz89uwYcPKlSvlHQt4d+/wn0v2XWAREwAAAAAAAGQF2TMAAAAAAACyguwZAAAAAAAAWUFRKQAAAADA/3N2dq6srJR3FGBAg7lnAAAAAAAAZAXZMwAAAAAAALKC7BkAAAAAAABZQfYMAAAAgA9vzZo148aNu3fvXq9bExMTjY2N09PT3/ModDqdRCLR6fT3HCcxMdHc3Ly0tLRfewkEgoULFzo4OEg/809aaWmpubl5YmIi+lIoFEZHR5uZmZFIpNDQ0PeMua6uzsHBITg4+D3H+SDeM5gP9T5+GpA9AwAAAODDc3Z2bm5uvnnzZs9NfD7/6tWrZDLZzs6uv8O2trampKScPn36Q8T4qeXl5R04cIBKpcbFxf3www+VlZXh4eEcDkfecYH+gewZAAAAAB+enZ0dmUzOy8trbGzstunZs2fPnz93dnbW0NDo77Dl5eXbt29vampCX6JLZAzYx1BTKJSSkhLJYwvLy8uVlZX9/f1nzZo1evTo/fv35+bmfiVPff6SQPYMAAAAgA9PXV3dzs7u6dOnz54967YpNzcXQRAnJyd5xCVnGAxm0CDIvj5v8P4BAAAA4MPDYDCzZs1SUFDIzMyUbudyuX///beVldWYMWMQBBEKhcePH6dSqSQSyczMzN/fn8VioT3RquJ169YdOXLEzMyMQqH89ttvHh4efD4/OjoaLVPuVi/b2tp67NgxyWi+vr6S3F0kEmVkZLi5uaFlxxQKhUajVVVVyXIuLBZrzZo1FAqFRCJZWlpGRkZKJr9RT58+9fb2JpPJ3U5BUveMlgVHR0fz+XwPDw97e/u5c+devHixurrazs5OUi5cVVXl6+uLRkilUtPS0kQikeQoTU1NkZGRFArF2NjY1dWVwWD0ETNayU2n0/39/clkMplMXrZsmfT5sliskJAQGxsbEolkbGzs5OR0/PhxoVDY65VPS0tDEOTZs2c0Gs3S0pJEIpHJZFdX16ysLOm5c7FYnJ6ejl5/KpUqGRD17Nkz6bM7duxYa2trr8Gj7+OUKVPIZDJ6zUNCQgZOiQs8LQUAAAAYSF68eJe9Ro4cgEcxMTEhk8l3797lcrlqampoY2lpaUVFhbe3Nx6PFwqFYWFhZ8+epVAo/v7+HA4nOTl56dKlycnJurq6aH86nf7PP/9s3bq1traWSqUOHz58z549M2bMmDFjhp6eXm1treRwQqHw119/TUlJoVKpwcHBTCYzOTl50aJFR48eHTt27JEjR2JiYmxsbCIiIgYPHkyn03Nycl69enXixAlVVdU+zoLD4dBotMbGxp9++snQ0LCgoOD06dNMJjMuLg7twGQyaTSam5vbolNWVawAACAASURBVEWLbt26deHChZqamuTkZCKRKBmESCSGh4enp6dnZ2cHBASMGjUKh8MlJCRUVFSsW7fO1NQUQZAHDx7QaLS2trYFCxaYm5unpqYGBwez2WwajYbBYPh8/urVq+/cuePu7m5vb3/z5s0NGzYIhUJra+s3Rd7W1rZ+/XoDA4Nt27ax2ewjR47Mnz8fvRo1NTUrVqyor6+fN2/e2LFjX758mZKSgl4ZLy+vnleeQqGUlZUtW7ZsyJAhNBrN0NCwrKzs/PnzgYGBqqqqkvp1Op2el5c3a9Ysc3PzCxcuhIeHv3jxYsuWLRgMJisra8OGDYMHD169erWenl5qampkZGRRUVFUVBSBQJAOu7Oz87fffktJSZk+fbq/v397e3t6evr58+cbGhri4uIGDx4s27++jwiyZwAAAGAgMTJ6l736Wzv7DkdZuhQ5erRfexCJRA8Pj99++620tNTBwQFBELFYnJubO2LECLRs4/bt2xcuXPj++++3b9+Ow+EQBKFSqTQaLTo6eufOneggbW1tmzdvRndHEERJSSkhIcHExGTatGndDoeO9vPPPwcFBWEwGARBJk2atHr16tzcXF1d3by8PHt7+/j4eDwejyCIh4dHREREamoqk8nsO3suKyt7+vRpfHy8i4sLgiCurq5Dhgy5cuVKdXW1jo4O2mf79u1z5sxBEGTmzJlKSkqpqakvXrygUCiSQfB4vJOT09OnT69duzZp0iR0U3p6+qtXr7777rsRI0a0trbu3r27o6Pj+PHjlpaWCIK4ubmFhYXFx8ePHz9+/Pjx169fZzAY69evR5NpDw8PU1PTHTt29BG5UCikUCj79u1D8/jJkycvXbo0KSlp586dRUVFtbW1u3fvllzYKVOmLF68uLCwUJI9d7vyu3fvVlRUPHjwIJrru7m52dnZ+fn5PXjwQJI9t7e3//777+iFcnNz27RpU3p6upeXl46OzqFDh0aMGHHs2DE9PT30+icmJsbGxk6bNm3WrFnSYVdXVxcVFS1atCgsLAx9H93d3X/66afHjx83NjaOGDGij1P+NKByAwAAAPjKvNvEcz9TZ9SECRNUVFQk98Yxmcxr165ZWVlpa2sjCJKdnY3FYufPn4+mzgiCmJubOzo6FhUV1dTUoC1aWlqjR4+W5VjXr19XUVFxd3dHUy4EQSwtLW/duuXv76+qqnry5MnDhw+jqTOCIBgMRktLS5Zhhw4dqqysnJiYWFhYKBQKMRjMxo0br127ZmJignbQ0dGRpI8YDMbW1pbP50tPisuiqqqqtLTU3t5eknPjcLgFCxZgMBj06uXm5mpqas6cORM9OwwGM3PmTEn63iscDrdixQrJFDiFQrG3ty8rK+PxeO7u7sXFxZLMGEEQVVXVIUOGSO/e7cqvXbv21q1baOqMUlNTU1JSkt7Fzs7O0dFRcnQPD4+mpqb8/PwnT548fvzYxcUFTZ3R+N3c3LS0tHJycjo7O6UHMTIyys7ODg8Pl7yPeDxeXV39bZfw04G5ZwAAAOAz19+yjXeb3n4nRkZGEyZMYDAY9fX1GhoaDx484HA4c+bMUVBQaG5uZrFYysrKFRUV0usli0QiPp/P4/HQYg9tbe1uWd2b8Pl8PB6voqLypg4ikYjNZj9+/LiysjI/P7+4uFiWG/jGjRu3aNGiQ4cOeXl5YbHYsWPHent7u7i4DB06FO0waNAgBYX/JlSSbwL9Ultb29DQoKiomJOTI31GioqKNTU1zc3NbDZbX19fclAEQYYOHaqvr9/HmEpKSpKCGQRBFBQUNDQ0bt68yWaz0dVOBAJBeXn5ixcvCgsLb9++zWQypetAer3yTU1Njx49evny5d27dxkMBp/Pl96qrq4u+X6CIIiKioqSklJ5ebmhoWFbW5uFhYV0ZzU1NUNDQy6X29bW1jN4oVDIZDKfP3/+8OHDmzdvPnr0SFNTs4+T/ZQgewYAAAA+c7Ld+iYXCgoKs2bNysnJefTo0aRJk3JyckaPHo1mUWKxuLOz8/Xr15s2beq5I4fDMTY2RhDkg6xQIRaLr127FhISwuVyEQRRUVGhUCgyPh4Fh8Nt3Lhx8eLFmZmZWVlZjx49Cg0N3bVr19GjRw0MDN4/NpRIJBKLxZcuXbp06VK3TWw2u7m5+UMdSEFBAYvF8ni8rVu3ZmZmisViLBZrYGBgaWmJXhyJbleeyWSuW7eusLAQQRBFRUVjY2MrK6u///77rUfsNj8traurq+f7KxKJTp48GRsbi561urq6jY1NW1vbB7wI7wmyZwAAAGAg+QSp8KfNts3NzUeOHPnXX39pa2sXFBQsXLgQnR4mEAiGhobV1dUpKSm9ViAIBIJ+HYhIJLa2tkqXxjY2Ni5fvtzIyGjZsmW//PLLqFGjoqKiDAwMsFgsgiCJiYmyP1xQV1eXRqPRaDShUHju3LnIyMjMzEzJQs7vT0dHR1VVddmyZatXr+65VSwW6+rq3r59m8vlSu6x4/P5r1696qN4o62tTXqx7fb29urq6mHDhqmrq+/du/fq1auRkZEeHh7ogHV1dW96MCSCIK2trZGRkZWVlQcPHrS3t0dv3SstLe32NJyGhob29nbJjX2NjY1tbW2jRo1CJ6EfPHggvTI3l8utrq62tLTsll7fvn07KirK1dV1w4YNmpqaaP1GcHAwmrgPBFD3DAAAAAwkI0f2+88nOMQ7HOU/NDQ0JkyYUFRUlJ6eLhaL0VvKUBMnTqytrf3rr78kq57x+fwffvhhypQpb1pLDovFKigodKuURTk6OjY2NtLpdMloN27cKCsrGzdu3KtXrzgcDpVKNTIyQlNnHo93/fr1bvllr1JSUiZNmnT79m30JQ6HMzExwWKxfUypygiHw3V1daHnoq+vP3LkyMuXL0tWu0MQJCsri0Kh/PHHHxgMZvLkyWw2OyMjQ3J2d+7c+ffff/sYXygUXr58WbJm3KNHjwoLC+3t7YcMGfLkyRMNDQ0nJyc0dRaLxQwGg81mo+lvz6H4fP7Tp0+NjY3t7OzQ5FgkEuXl5XWr8C4sLHz06BH699bW1rNnzw4dOvTbb781MzMbPXp0VlYWk8lEt4rF4oyMDDabbW9vL133giDIw4cPOzo6pk6dqqWlhabOVVVVxcXF6Fejfl3hjwTmngEAAADwcc2cOTMtLS05OXn8+PHS1Q4zZsy4c+fOjh07bt265enp2dTUdPbs2adPn27cuHHkyJG9/qZeXV2dQCBkZmbq6enZ2tpKb5o4ceL3338fGxvLYDA8PT1LSkr+/PPP0aNHu7i4tLW16erqJiUlNTU1mZubl5WVpaam8ng8oVDYa9GtNEtLy87OzoCAAMnibqdOnSISiT0X/egvQ0PDixcvJicnf/fdd99+++2WLVtoNJqHh8fSpUsNDQ3v3LmTnp6upaU1f/589Fp5eXnFxsY+efLEycnp5s2bf/31F/pNoA8XLlxgs9nff/99eXn5sWPHtLS0aDQagUCwsbFhMBhBQUGenp4IgmRkZNy9e1csFre0tEiv0CyhpqZmYWHx119/bdiwYdq0aU1NTRcuXHjy5Am6lJ50z1WrVi1cuFBDQ+P06dNlZWUbN240MTHBYDC+vr4bNmyYPXv20qVL0RXr8vPzJ0+e7Orq2u1Y1tbWBAJh27ZtVVVV+vr6DAYjPT29vb1dSUnprW/WpwHZMwAAAAA+LlNTU1NT07t3737//ffSd5XhcLgtW7aYmpomJyevW7du0KBBZDIZXc5Zst5CNxoaGuiSdkFBQbt27ZJeKlgyWlJSUlBQkLKysru7e3BwMLogXUJCQkRExNGjR7u6ugwMDAIDA0kkkq+vb1lZWd8P+jYxMTl79uz27dtPnjzZ3NysrKxsZ2e3adMmIyOj/taWdOPu7n79+vXDhw8XFhYmJydbWFicOnUqJibmwIEDzc3NKioqbm5u/v7+6NLX6NkZGRkdPHgwPT1dR0cnIiKiZ5F0N7/++iu6zp2SkpL0aD/++COCIKdOnQoNDVVWVnZwcMjMzExMTGQwGDwer+cSfgoKCuHh4QQCIS0tLTs7W0VFxcPDY/fu3b/88ktVVZUkgXZ2dnZ0dPztt9/q6uqMjIzi4+Mlb6WLi4uxsXF0dHR8fHxHR4eOjs7WrVvnz58v/e8BZWVlFRcXFxUVtXPnzkGDBo0ZMyY2NrarqysgIKDbOoDygvlKnq6OLmm+Zs0aeQcCZFVdXa2trd3ttzlgwGpra+NwOH3f/Q0GlIaGBgRBhg0bJu9Avmrwswl8PImJidHR0QcPHuz7u8GX6h3+c8m+C9Q9AwAAAAAAICvIngEAAAAAAJAVZM8AAAAAAADICrJnAAAAAIAvzcqVKysrK7/OouePDbJnAAAAAAAAZAXZMwAAAAAAALKC7BkAAAAAAABZQfYMAAAAgI9IJBJlZWXNmTPHzMyMRCJRKBQajfbs2TNJBzqdTiKR6HS6LKP1q/N7Ki0tNTc3T0xM7O+OiYmJfQQpEAgWLly4cOFC9GErYrH45MmT48aNI5FIP/zwQ69PWOyX4OBgBweHurq69xzn/XU70/6qq6tzcHAIDg7+4IG9J3gUBQAAAAA+lpqamsDAwKKiorFjx27atGn48OFlZWXnz593c3PbsGGDr6/vm54p+PUoKyuLiYkxMjJatmyZvr7+oEGDUlJSRCLRwoUL5R0a6B1kzwAAAAD4KAQCQWhoaElJye7du2fOnIkmym5ubn5+fgEBATt37jQzM7O3t+/XmM7OzpWVlR8n3k+EQCCcPn1a8rK2tpbP569cudLFxQVBkNLS0u3bt//000/yCxC8BVRuAAAAAOCjyM3Nzc/Pp9FoktQZpaqqunr1al1d3c89D/6AcDicvEMAsoLsGQAAAAAfXmdnZ05ODoFAmDZtWs/yDFtb22vXrvn4+PTcsbW19dixY1OmTCGTySQSydLSMiQkhMPhoFul654TExPNzc3pdLq/v7+ZmRmZTF68eHFNTQ2TyfTz8yOTyWZmZkFBQXw+XzJ4VVWVr68vWoFNpVLT0tJEIpFkK4vFkgzl7e1dUVHRxwk2NTVFRkZaWlqixdxr1qxhsVg9O1AoFGNjY1dX19u3b4vFYkSqGri2tnbhwoV+fn4Igvj5+Zmbmx85csTDw4PP50dHR5ubm5eWlqL9d+zYYW1tjR4oMjKyqalJchSRSJSWlkalUkkkkrW1dVJSUkdHx5tiRq9eWlpaZGSkmZmZsbGxp6dnYWGhjBc/MTHRwcGBTqdTqVQymRwcHNzR0cFisUJCQmxsbEgkkrGxsZOT0/Hjx4VCofRxGQyGq6ursbGxtbX1jh07pMug0SOi8ZuZmfn6+krXxEsTiUQZGRlubm7SBfRVVVV9vEcfCVRuAAAAAANJRIS8I3hXDg6Io6PkFY/He/z4MYlEMjAwkH2Mzs7O3377LSUlZfr06f7+/u3t7enp6efPn29oaIiLixs8eHC3/m1tbSEhId98883vv/9eXFyckpLi6+vb1tZmaWkZExOTmZl5+fLlYcOGbdmyBYPBPHjwgEajtbW1LViwwNzcPDU1NTg4mM1m02g0DAbDYrGWLl3KZrMlWzdu3NjZ2dlrnK2trcHBwXfv3vXy8jI3Ny8vLz9y5Mjz58+PHTumoaGB9gkNDTUzM9u8ebNAIEhISFi5cuXRo0fHjx8vGURJSSkgIMDc3PzAgQM//vijpaWloaHhhg0b9uzZM2PGjBkzZujp6fH5/FWrVt26dYtKpXp6epaUlJw/f768vHzfvn1EIlEsFh8+fHjHjh1jx4719/fncDgHDx5sbGzU1tbu4yJv27YNj8eHhoYiCHLw4MElS5bEx8c7OzvLcvFra2s3bdo0d+5cTU1NDQ2N+vr6FStW1NfXz5s3b+zYsS9fvkxJSYmIiBg8eLCXlxd6uIcPH65bt87Z2dnPzy83N/fgwYMVFRVxcXF4PJ7P5wcEBNy4cYNKpQYHBzOZzOTk5Hnz5u3Zs8fBwaFb2EeOHImJibGxsUHHp9PpOTk5r169OnHihKqqquz/xt4fZM8AAADAQBIeLu8I3lV4uHT2LBaLOzs78Xg8FouVfYzq6uqioqJFixaFhYWhM9bu7u4//fTT48ePGxsbR4wY0a2/UCh0cnLavn07DoebOXPm69evMzMz169fv3LlSgwG4+zs7Ovr++jRo+bmZiwWu3v37o6OjuPHj1taWiII4ubmFhYWFh8fP378+PHjx58/f766uvqPP/5A64/RrWfPnu01zqqqqnv37tFotNWrV6Mturq6UVFRz58/l2TP06ZN27VrF1qSMWrUKD8/v8LCQunsGYvF2tnZoROx48ePR58L2NHRkZCQYGJiMm3aNARBjh8/np+fLzmj2bNn29jYBAYGHj58eO3atUwm88SJE5MmTUKTaQRBqFQqjUbr+yKrqKgkJyfr6uoiCDJlyhQfH5+EhARbW9v6+vq3XvyOjg5XV9f169ejHdLS0mpra3fv3i1JdqdMmbJ48eLCwkJJ9iwQCDZu3Ih+RfHw8DAzM9u9e3dBQYGDg8P169dv3LgRHByMnh2CILNnz/bx8dmzZ4+VlZV0zDweLy8vz97ePj4+Ho/HIwji4eERERGRmprKZDI/cfYMlRsAAAAAGCiMjIyys7PDw8MlxR54PF5dXb2PXb777js0Q1VQUBg7diyBQJg4cSK6u7Kyso6OzqtXr1paWqqqqkpLS+3t7SkUCrojDodbsGABBoPJzc0VCAQMBsPCwkJyFyMOh/Py8iIQCL0elEgkDhky5Ny5c1lZWe3t7QiCzJ079969exMnTpT0cXV1lVQzk8nkESNGlJeX9+tqNDc30+l0bW1tNzc3yQWxt7e3srLKy8trbGwsKytjsVgLFixAU2cEQczNzd96I+aSJUvQ1BlBED09PRcXlxcvXlRXV8t48alUqqSDu7t7cXGx9DyxqqrqkCFDpPuTyWRPT090F/QrjYqKSnZ2Nlrbo6WlJX12aDyPHz9+8uSJ9CCqqqonT548fPgwmjqjQ2lpab31Gn4MMPcMAAAAgA9PQUFBWVm5tbVVurBYRkKhkMlkPn/+/OHDhzdv3nz06JGmpuabOne73w6DwQwaNKjn32traxsaGhQVFXNyciSd+Xy+oqJiTU1NS0vLq1evrK2tpdNlbW3tN01q6unp0Wi0mJiYVatWYTAYY2PjuXPnzp49W3p2XDowBQUFSSSya2lpYbFYysrKRUVFaA00qqurq76+vrm5+eXLl0QiUU9PT/r0TUxM7t2718ewOjo60i+1tbV5PF5NTc2YMWOQt118AoEgmVyXEAgE5eXlL168KCwsvH37NpPJtLa2lmxVU1OTpLwIgqioqODxeBaLxePxuFyuoaGhmpqa9GgWFhZtbW2NjY09IxeJRGw2+/Hjx5WVlfn5+cXFxe9wVd8fZM8AAADAQLJ0qbwjeFeGhtKvVFVVv/nmmytXrvz777+S6V4JLpf7008/jRkzZt26ddLtIpHo5MmTsbGx6END1NXVbWxs2tra3v8ZIiKRSCwWX7p06dKlS902sdnslpaWfo2GwWB++OGHWbNmXblyJSMjo7i4+Pfff9+7d+8ff/yBFmB8EGj1S1VVVc8nhhCJxNevX3+oA2EwGCwWK8vFl/5CgiAIj8fbunVrZmamWCzGYrEGBgaWlpZcLvetR1RUVHxT4tvtjkOUWCy+du1aSEgIOriKigqFQpHcWPmJQfYMAAAADCRHj8o7gg8Dg8FMnjz54sWLV65cGTt2bLdlN+7evfvgwYPRo0crKytLt9++fTsqKsrV1XXDhg2amproXsHBwdLrQrwbHR0dVVXVZcuWSSqVpQkEAl1d3YqKisbGRhUVFbQRna7uY0xVVVUvLy8vLy+RSJSXlxcYGHjp0iVHqeLv96SsrGxoaKitrX3o0KFea0hqa2sFAkFFRYXk+4lYLO57qRB0L+mX5eXlw4YN09TU7O/FF4vFe/fuvXr1amRkpIeHBxphXV1dt5nvhoYG6WVAGhsbW1tb9fX1VVRU1NTUiouLuVyu9Nk9fPhQSUlJ8i6gnj9//ssvv4waNSoqKsrAwAAtpk9MTJRL9gx1zwAAAAD4KJycnKhUalJS0l9//YUu1oZ6/vx5bGzssGHDFi5c2C2rfvjwYUdHx9SpU7W0tNBNVVVVxcXFra2tvf4qX3b6+vojR468fPmy9LpyWVlZFArljz/+IBAINjY2jx49unHjBrpJLBZfuXJFerU7abdv37a1tf3zzz/Rl1gsdtSoUQQCQVFRsV93SfaExWIVFBTQtT6UlZWtrKwePHhw8+ZNSQcWizV16lRvb28ej2dqaqqjo3P27FlJnC9evLhz507fh0hPT5f0ZzKZN27coFAoRkZG/b34zc3NT5480dDQcHJyQtNfsVjMYDDYbHZDQwNaDo4gSEVFxa1bt9C/i0Si1NTUxsZGR0dHBQWF6dOns9nsjIwMyT8PJpOZlZVFIpFGjRolfax///2Xw+FQqVQjIyP0CvN4vOvXr7+pxuOjgrlnAAAAAHwUBAJh+/btNBpt7dq1hw4d+v7771VVVe/cuZOeno4gSHR0tImJSbdd0Mrjbdu2VVVV6evrMxiM9PT09vZ2JSWltra29wmGSCRu2bKFRqN5eHgsXbrU0NAQjURLS2v+/PkIgqxYseL+/fvr168vKiqytLRMTU1lMBhvepA4mUwePnx4RETE/fv3J0yYwOPxTp48+fr1a8ntce9MXV2dQCBkZmbq6enZ2tqiUQUEBLi7uzs6OlZXV6ekpNTW1gYFBamqqqqqqm7atCkwMNDLy8vHx4fD4SQnJ/P5/L5vpysoKED7o0vpYTCYtWvX4vH4/l589CsHg8EICgry9PREECQjI+Pu3btisbilpUVSgKGkpBQZGXn//n10HcD8/HwvLy/09kpHR8fJkyfHxsYyGAxPT090xbr29vbo6GhVVdW6ujrJsUxNTXV1dZOSkpqamszNzcvKylJTU3k8nlAofOM/jORkZM2ad30f+gLZMwAAAAA+Fl1d3QsXLpw7d+748eO//vqrSCRSUVFxc3Pz9/eXLPsgzcrKKi4uLioqaufOnYMGDRozZkxsbGxXV1dAQMCLFy961k/3i4WFxalTp2JiYg4cONDc3NwtEiKRGB8fv3v37vPnz588edLU1DQmJmbnzp29DqWhoXHs2LGdO3dmZWWdPXtWUVHR3Nz8t99+k75b7t1oaGjQaLTo6OigoKBdu3bNnj07Pj4+ISHh8uXLqamp6IFiYmIkB5oxY4aKisq2bds2bdo0ZMiQ+fPnDxkyJC0trY9DrFq1qrm5OSwsDEEQKpW6YcMG9GvMO1z8H3/8EUGQU6dOhYaGKisrOzg4ZGZmJiYmMhgMHo+H3nP5zTffLF++PDY29tixYyNGjAgLC1uwYAF6SyWRSNy/f/+5c+eSkpKCgoIUFRWl45Gmr6+fkJAQERFx9OjRrq4uAwODwMBAEonk6+tbVlbWe635ixeIkxOSm9v/N+EtMNK/SfmCxcXFIQiy5uN8BQEfQ3V1tba2toICfMH7PLS1tXE4HH19fXkHAmSFVnMOGzZM3oF81eBnE/jE6HS6n5/fhg0bVq5cKe9YPq64uDgkPHxNQwMSHo6Ehcm6i2z/H6HuGQAAAAAAfKHCw5Hr1z/skJA9AwAAAACAL9eyZR92PMieAQAAAADAlwstgP5woKgUAAAAAOCr4OzsXFlZKe8o5OH6deT6deQDLcUNc88AAAAAAOCL0+2xnU5OH6oAGuaeAQAAALlhMBjyDgGALxCDwbCzs0Nyc/+nZiMi4oNMP8PcMwAAACAftra2dnZ2MnYWCATo8+fAZ6Gzs1MgEMg7iq+XnZ2dra0t4uj4P+ny9esf5A5CmHsGAAAA5MPOzk727BlWwf+8wCr4AwU6/Syp2UhORnx83nMGGuaeAQAAAADAl+vo0f956eSEvHjxPuNB9gwAAAAAAL5cI0d2T6CXL3+f8SB7BgAAAAAAX7SlS/+nWiM3F4mIeOfBIHsGAAAAAABfutxcZOTI/758jyd4Q/YMAAAAAAC+At3qN951/Q3InsEAVVJSIu8QQD+w2eza2lp5RwH6gc1ms9lseUcB+gE+FT8v8Kk4EDk6IuHh/335rk/whuwZDFDR0dHwo/0zwmazg4KC5B0F6IecnJycnBx5RwH6AT4VPy/wqThAhYV1XwG6//Ub8sye6XS6ra1taWlpt/bW1takpCRra2sSiUShUEJCQjgcTrc+LBbL39/fzMyMRCJRqdTjx48LhcJPFTgAAAAAAPg89VzArp8JtNyy56qqqh07drS1tXVrFwgEq1evjoqKGjp06Pz580kk0vnz5xcuXMhisSR9Hj16NGfOnOzsbCsrqzlz5nR2doaHh4eFhUECDQAAAAAA+jJyJJKb+z8t/SyAlk/2XFJS4uPjU1FR0XPTlStXrl+/7u3tnZ2d/fvvv1+6dGnjxo2VlZWHDx8Wi8UIggiFwoSEhMbGxj179pw+fTo2Nvbq1atUKvXixYsMBuOTnwoAAAAAAPis9CyA7k8C/amz59bW1oMHDy5evLi9vd3IyKjn1rS0NDU1NR8fHxwOhyAIBoNZsGCBhYVFbm4uWu9VWVnJYDDs7Owc/1O2QiQS16xZo6iomJaWhmbYAAAAAAAAvFG3AujkZNnrNz519nzr1q3ff/9dV1f35MmTlpaW3bZyOJznz58bGxvr6upKGolE4rhx42pqatC56sePH79+/frbb7/F4/GSPkZGRnp6eg8fPuTxeJ/mRAAAAAAAwGfsfwug11y6JON+nzp7VlJSCgkJSU1NJZPJPbc2NjYKBAI9PT0CgSDdrqmpKRQK6+vrEQRBZ6DNzMykOygqKg4bNgzd/WOGDwAAAAAAvgg9n+Atm0+dPVOpVD8/P+lpY2n19fW9pr+GhobIf/Lmly9f9uygrKysbtxffwAAECxJREFUpaUlEAgaGxs/aLwAAAAAAOAL1e0J3rJR+AiBvDuRSNRr4TJaA43qdWENDAYzaNBbvgnAPYWfFyaTeeHCBXlHAWTFZDKZTGZcXJy8AwGygo/Ezw58Kn5e4FPxszF79vf5+XqdnbLvMbCyZywWi8FgerZLZ8zSmbSEWCzu6urqY2RbW9v3Dw98SmvWrJF3CKAf9PT04C37vNjZ2ck7BNA/8F/s8wKfip+RC7Gx6F9kTBc/SvZcV1c3b9686upqScucOXNi/xNZH9TV1btVPKPQag0tLS3kP1Uc3TQ3N7PZbAKBoKKi0uvIdnZ28KMCAAAAAAC8p4H1pO7hw4cPHTq0pqamW/VzbW0tDodTV1dH/pM9l5eXS3fo6OhoaGhQUVHpNfkGAAAAAADgg/goc88jRozIy8t7hx2HDx9uampaUlLCYrFMTU3RxsbGxgcPHujo6BgbGyMIMmrUKHV1dQaD4ePjI7n7sKKi4sWLF25ubqqqqh/qLAAAAAAAAOhmYM09Dx482MnJicvlJicnt7a2IggiFotTUlL++ecfJycntHJDT0/PwsKCwWDQ6XT0FkM+n793796uri53d/dey6YBAAAAA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equation","description":"A conic of revolution (around the |z| axis) can be defined by the equation\r\n\r\n   s^2 – 2*R*z + (k+1)*z^2 = 0\r\n\r\nwhere |s^2=x^2+y^2|, |R| is the vertex radius of curvature, and |k| is the conic constant: |k\u003c-1| for a hyperbola, |k=-1| for a parabola, |-1\u003ck\u003c0| for a tall ellipse, |k=0| for a sphere, and |k\u003e0| for a short ellipse.\r\n\r\nWrite a function |z=conic(s,R,k)| to calculate height |z| as a function of radius |s| for given |R| and |k|.  Choose the branch of the solution that gives |z=s^2/(2*R)+...| for small values of |s|.  This defines a concave surface for |R\u003e0| and a convex surface for |R\u003c0|.  \r\n\r\nThe trick is to get full machine precision for all values of |s| and |R|.  The test suite will require a relative error less than |4*eps|, where |eps| is the machine precision.\r\n\r\nHint (added 2015/09/03): the straightforward solution is \r\n\r\n   z = (R-sqrt(R^2-(k+1)*s^2))/(k+1), \r\n\r\nbut this does not work if |k=-1|, gives the wrong branch of the solution if |R\u003c0|, and is subject to severe roundoff error if |s^2| is small compared to |R^2|.  It is possible, however, to find a mathematically equivalent form of the solution that solves all three problems at once.\r\n","description_html":"\u003cp\u003eA conic of revolution (around the \u003ctt\u003ez\u003c/tt\u003e axis) can be defined by the equation\u003c/p\u003e\u003cpre\u003e   s^2 – 2*R*z + (k+1)*z^2 = 0\u003c/pre\u003e\u003cp\u003ewhere \u003ctt\u003es^2=x^2+y^2\u003c/tt\u003e, \u003ctt\u003eR\u003c/tt\u003e is the vertex radius of curvature, and \u003ctt\u003ek\u003c/tt\u003e is the conic constant: \u003ctt\u003ek\u0026lt;-1\u003c/tt\u003e for a hyperbola, \u003ctt\u003ek=-1\u003c/tt\u003e for a parabola, \u003ctt\u003e-1\u0026lt;k\u0026lt;0\u003c/tt\u003e for a tall ellipse, \u003ctt\u003ek=0\u003c/tt\u003e for a sphere, and \u003ctt\u003ek\u0026gt;0\u003c/tt\u003e for a short ellipse.\u003c/p\u003e\u003cp\u003eWrite a function \u003ctt\u003ez=conic(s,R,k)\u003c/tt\u003e to calculate height \u003ctt\u003ez\u003c/tt\u003e as a function of radius \u003ctt\u003es\u003c/tt\u003e for given \u003ctt\u003eR\u003c/tt\u003e and \u003ctt\u003ek\u003c/tt\u003e.  Choose the branch of the solution that gives \u003ctt\u003ez=s^2/(2*R)+...\u003c/tt\u003e for small values of \u003ctt\u003es\u003c/tt\u003e.  This defines a concave surface for \u003ctt\u003eR\u0026gt;0\u003c/tt\u003e and a convex surface for \u003ctt\u003eR\u0026lt;0\u003c/tt\u003e.\u003c/p\u003e\u003cp\u003eThe trick is to get full machine precision for all values of \u003ctt\u003es\u003c/tt\u003e and \u003ctt\u003eR\u003c/tt\u003e.  The test suite will require a relative error less than \u003ctt\u003e4*eps\u003c/tt\u003e, where \u003ctt\u003eeps\u003c/tt\u003e is the machine precision.\u003c/p\u003e\u003cp\u003eHint (added 2015/09/03): the straightforward solution is\u003c/p\u003e\u003cpre\u003e   z = (R-sqrt(R^2-(k+1)*s^2))/(k+1), \u003c/pre\u003e\u003cp\u003ebut this does not work if \u003ctt\u003ek=-1\u003c/tt\u003e, gives the wrong branch of the solution if \u003ctt\u003eR\u0026lt;0\u003c/tt\u003e, and is subject to severe roundoff error if \u003ctt\u003es^2\u003c/tt\u003e is small compared to \u003ctt\u003eR^2\u003c/tt\u003e.  It is possible, however, to find a mathematically equivalent form of the solution that solves all three problems at once.\u003c/p\u003e","function_template":"function z=conic(s,R,k)\r\nz=0;\r\nend","test_suite":"%%\r\nR=5;\r\nk=-1;\r\ns=-5:5;\r\nz=[25 16 9 4 1 0 1 4 9 16 25]/10;\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=-5;\r\nk=-1;\r\ns=-5:5;\r\nz=-[25 16 9 4 1 0 1 4 9 16 25]/10;\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=6;\r\nk=0;\r\ns=0:0.125:2;\r\nz=[0 0.001302224649086391 0.005210595859100573 ...\r\n   0.01173021649825800 0.02086962844930099 ...\r\n   0.03264086885999461 0.04705955010467117 ...\r\n   0.06414496470811713 0.08392021690038396 ...\r\n   0.1064123829368584 0.1316527028472488 ...\r\n   0.1596768068881667 0.1905249806888747 ...\r\n   0.2242424739260392 0.2608798583755018 ...\r\n   0.3004934424110011 0.3431457505076198];\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=6800;\r\nk=-2;\r\ns=10.^(-9:9);\r\nz=[7.352941176470588e-23 7.352941176470588e-21 ...\r\n   7.352941176470588e-19 7.352941176470588e-17 ...\r\n   7.352941176470588e-15 7.352941176470588e-13 ...\r\n   7.352941176470548e-11 7.352941176466613e-9 ...\r\n   7.352941176073046e-7 0.00007352941136716365 ...\r\n   0.007352937201052538 0.7352543677216725 ...\r\n   73.13611097583313 5292.973166264779 93430.93334894173 ...\r\n   993223.1197327390 9.993202311999733e6 9.99932002312e7 ...\r\n   9.9999320002312e8];\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=exp(1);\r\nk=pi;\r\ns=10.^(-7:0);\r\nz=[1.839397205857214e-15 1.839397205857469e-13 ...\r\n   1.839397205882986e-11 1.839397208434684e-09 ...\r\n   1.839397463604480e-07 0.00001839422981299153 ...\r\n   0.001841981926630790 0.2212216213343403];\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nt=fileread('conic.m');\r\nassert(isempty(findstr(t,'roots')))\r\nassert(isempty(findstr(t,'fzero')))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":245,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":37,"created_at":"2015-08-26T21:39:35.000Z","updated_at":"2026-02-08T12:47:36.000Z","published_at":"2015-08-26T22:21:10.000Z","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\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"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\\n\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\u003eA conic of revolution (around the\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e axis) can be defined by the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   s^2 – 2*R*z + (k+1)*z^2 = 0]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es^2=x^2+y^2\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:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the vertex radius of curvature, and\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the conic constant:\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u0026lt;-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a hyperbola,\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek=-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a parabola,\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-1\u0026lt;k\u0026lt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a tall ellipse,\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek=0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a sphere, and\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u0026gt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a short ellipse.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez=conic(s,R,k)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to calculate height\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as a function of radius\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for given\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Choose the branch of the solution that gives\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez=s^2/(2*R)+...\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for small values of\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. This defines a concave surface for\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u0026gt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and a convex surface for\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u0026lt;0\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=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe trick is to get full machine precision for all values of\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The test suite will require a relative error less than\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e4*eps\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eeps\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the machine precision.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint (added 2015/09/03): the straightforward solution is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   z = (R-sqrt(R^2-(k+1)*s^2))/(k+1),]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebut this does not work if\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek=-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, gives the wrong branch of the solution if\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u0026lt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and is subject to severe roundoff error if\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is small compared to\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. 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