Vertex form is a(x-h)² + k. The vertex is (h, k), and the sign of a tells whether the parabola opens up or down.

What is the conversion formula?

For ax² + bx + c with a non-zero, h = -b/(2a) and k = c - b²/(4a). The calculator shows the resulting form and vertex.

Why does a equal zero get rejected?

When a is zero the equation is linear or constant, not a parabola. This page rejects that input rather than inventing a vertex.

Vertex Form Calculator

Convert ax² + bx + c to a(x-h)² + k. This page starts in vertex-form mode with a worked quadratic, shows h and k, and draws the parabola so the algebraic form has a visual check.

Vertex form(x-2)² + 3Vertex (2, 3)

Common questions

What is vertex form?: Vertex form is a(x-h)² + k. The vertex is (h, k), and the sign of a tells whether the parabola opens up or down.
What is the conversion formula?: For ax² + bx + c with a non-zero, h = -b/(2a) and k = c - b²/(4a). The calculator shows the resulting form and vertex.
Why does a equal zero get rejected?: When a is zero the equation is linear or constant, not a parabola. This page rejects that input rather than inventing a vertex.

Uses the stable quadratic formulation for finite decimal coefficients up to 10^100. Roots and the discriminant are approximately represented in JavaScript, and each result includes a normalized substitution check; this calculator describes algebra and gives no advice about what a result means.