Quadratic Vertex Form Converter

About this calculator

Every quadratic written in standard form, ax² + bx + c, can be rewritten in vertex form, a(x − h)² + k, where (h, k) is the parabola's vertex — its minimum point if a > 0 or maximum point if a < 0. The conversion is done by completing the square: h = −b/(2a) and k = c − b²/(4a), which directly exposes the graph's turning point without plotting anything.

Vertex form is the version algebra and precalculus students reach for when graphing a parabola by hand, finding the axis of symmetry, or solving optimization problems like maximizing area or revenue, since the vertex coordinates are read off immediately instead of derived by taking a derivative or completing the square from scratch each time.

This calculator takes your coefficients a, b, and c, completes the square automatically, and returns the equivalent vertex-form expression along with the vertex coordinates — useful for students checking homework, teachers preparing examples, and anyone verifying a graphing calculator's output.