Completing the Square Calculator

Rewrite ax² + bx + c in vertex form a(x − h)² + k.

h (vertex x) 3

k (vertex y) 2

Formula: a(x − h)² + k with h = −b/2a, k = c − b²/4a

Step-by-step with your numbers:

1. Values used:

2. a = 1

3. b = -6

4. c = 11

6. h (vertex x) = 3

7. k (vertex y) = 2

Did we solve your problem today?

Completing the square turns a quadratic into vertex form, revealing its turning point.

The math behind it

ax² + bx + c = a(x − h)² + k where h = −b/(2a) and k = c − b²/(4a). The vertex of the parabola is (h, k).

x² − 6x + 11 = (x − 3)² + 2, so the vertex is (3, 2).

Why complete the square?

It makes solving, graphing and integrating quadratics much easier and exposes the vertex directly.