Complete the square calculator

Completing the square

Rewrite ax² + bx + c in the form a(x − h)² + k. This reveals the vertex (h, k) of the parabola.

Steps

1. Factor out a from x² and x terms. 2. Take half of b/a, square it, add and subtract inside. 3. Factor the perfect square trinomial.

Example

x² + 6x + 2: half of 6 = 3, 3² = 9. x² + 6x + 9 − 9 + 2 = (x+3)² − 7. Vertex at (−3, −7).