Completing the Square Calculator

About this calculator

Completing the square rewrites a quadratic ax² + bx + c into vertex form a(x − h)² + k, where h = −b/2a and k = c − b²/4a. In this form, (h, k) is the vertex of the parabola — its minimum point if a > 0, or maximum point if a < 0 — which is far easier to read off than from the original expanded form.

Algebra students and teachers use this technique to graph parabolas by finding the vertex directly, and it's also the method used to derive the quadratic formula itself, making it a foundational skill that shows up throughout algebra and pre-calculus coursework.