Quadratic workbook

Completing the Square

A step-by-step method for converting a quadratic from standard form into vertex form — revealing the vertex directly from the equation.

Why complete the square? It's the algebraic bridge between standard form and vertex form — and it's also the technique behind the quadratic formula. There are two common ways to approach it depending on what you're trying to find.
ax² + bx + c  →  a(x − h)² + k adjust the sliders below to follow along with real numbers
Starting from f(x) = ax² + bx + c, rewrite in vertex form f(x) = a(x − h)² + k. The vertex (h, k) is read directly from the result. Use this when you want to graph the parabola or find its maximum or minimum.
a — x² coefficient 2
b — x coefficient −4
c — constant term 1
f(x) = 2x² − 4x + 1