Quadratic and completing-square calculator

For ax²+bx+c, completing the square gives a(x−h)²+k, where h=−b/(2a) and k=c−b²/(4a). The discriminant b²−4ac determines two real roots, a repeated root or complex conjugate roots. For x²−5x+6, the roots are 2 and 3 and the vertex is (2.5, −0.25).

The result above uses these exact values. This snapshot is included when the page is printed so the output can be checked against the original measurements.

Coefficient a

1

Coefficient b

-5

Coefficient c

6

Graph half-width around vertex

5

Primary result: Vertex x: 2.5.

• Check the selected mode, units and input values before using the result.
• Read the assumptions and rounding rules; compare the worked example with your intended calculation.
• A numerical result does not supply missing context or change the stated limitations.

Coefficient a must be nonzero. Coefficients are bounded to magnitude 1e100 and results use floating-point arithmetic. Nearly repeated roots are sensitive to rounding. This tool solves entered coefficients; it does not infer a missing equation from a worksheet image.