O Level Mathematics Home Tutors in DHA Islamabad for Cambridge Students

Factorising finds roots. Completing the square rewrites the quadratic so the vertex is visible without graphing.

Idea

x² + 6x + 5 becomes (x + 3)² − 9 + 5 = (x + 3)² − 4. The minimum is −4 when x = −3 — the turning point is (−3, −4).

Vertex form y = a(x − h)² + k makes (h, k) obvious. That is why the method is taught: not as a trick, but as a rewriting that exposes structure.

O Level Mathematics tutors in DHA Islamabad can pair one complete-the-square rewrite with a quick sketch of the same parabola.