Completing the square

What is completing the square?

Completing the square rewrites a quadratic ax² + bx + c into the form a(x + p)² + q. It exposes the minimum/maximum point of the parabola (at x = −p, y = q) and provides a route to the quadratic formula. GCSE Higher and A-Level both examine it — typical questions ask to express in completed-square form, find the turning point, or sketch the curve.