What this calculator does
Rewrite a quadratic in vertex form and calculate its vertex and roots.
How it works
The calculator evaluates ax² + bx + c = a(x + b/2a)² + c − b²/4a. Inputs are checked before calculation, and invalid values such as zero denominators or out-of-range selections produce a clear error instead of a misleading result.
Input query strings and outputs
Use an input name in this page’s URL as ?name=value, and join additional inputs with &. Portable shared links may instead use the compact ?ac= state parameter.
Input query strings
3-
?a=Coefficient aNumber · Required · Default: 1
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?b=Coefficient bNumber · Required · Default: 6
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?c=Coefficient cNumber · Required · Default: 5
Outputs
4-
vertexFormVertex formText · Primary output
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vertexVertex (h, k)Text
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discriminantDiscriminantNumber
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rootsRootsText
Inputs and results
The inputs are Coefficient a, Coefficient b, Coefficient c. Results include Vertex form, Vertex (h, k), Discriminant, Roots.