Vertex form calculator

Convert ax² + bx + c into a(x − h)² + k, where h = −b/(2a) and k = c − b²/(4a).

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Quadratic coefficient a

Linear coefficient b

More inputs and assumptions

Constant c

Answer

…

Convert ax² + bx + c into a(x − h)² + k, where h = −b/(2a) and k = c − b²/(4a).

More results

Precision and calculation record

Decimal places in numeric results and text downloads

Rounding changes displayed numbers, not the calculation. Text, fractions, matrices and CSV schedules keep their own formatting. Automatic keeps up to 12 significant digits, with money shown to cents where applicable.

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Formula and assumptions

The leading coefficient must be nonzero. Real coefficient inputs produce a real vertex even when there are no real roots.

Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.

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Updated 2026-09-26

Using Vertex form calculator

Convert ax² + bx + c into a(x − h)² + k, where h = −b/(2a) and k = c − b²/(4a).

The leading coefficient must be nonzero. Real coefficient inputs produce a real vertex even when there are no real roots.

Next: Quadratic equation solver

A worked example

Example inputs: quadratic coefficient a = 1, linear coefficient b = -4, constant c = 3. Vertex x coordinate = 2.

Before you use the result

The leading coefficient must be nonzero. Real coefficient inputs produce a real vertex even when there are no real roots.

Example results for quadratic coefficient a

These examples use Linear coefficient b: -4; Constant c: 3. They are reference calculations, not recommended settings.

Quadratic coefficient a	Vertex x coordinate
0.5	4
1	2
2	1

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