Problem 42840. Coefficients and vertex of a parabola given 3 points

Created by Roche de Guzman

Solve Later

{"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":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>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].</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![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)]]></w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

122 Solutions
19 Solvers

Last Solution submitted on Feb 25, 2023

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

Peng Liu on 29 Apr 2016

It would be better to add more test cases to reinforce the test suite.

Roche de Guzman on 1 May 2016

Thanks I just updated!

Solution Comments

Solution 886998

1 Comment

1 Comment

James on 6 May 2016

Using without the "round" fudge on the polyfit function should work, but gives errors on the order of 1e-14. Round only works because all the coefficients in your test suite are integers.

Problem Recent Solvers19

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!