Algebra
Intermediate

Completing the Square

Rewrites a quadratic in vertex form.

Formula

ax2+bx+c=a(x+b2a)2+c−b24aax^2+bx+c = a\left(x+\frac{b}{2a}\right)^2 + c - \frac{b^2}{4a}

Variables

a, b, cCoefficients

Example

x² + 6x + 5 = (x+3)² − 4, so the vertex is at x = −3.

Did You Know?

Completing the square is how the quadratic formula was originally derived — geometrically, you literally complete a square shape.

quadraticvertexalgebra