Cambridge IGCSE Additional Mathematics · Syllabus 0606 · Quadratic Functions
Completing the Square
What is Completing the Square?
An algebraic rearrangement that rewrites a quadratic ax^2 + bx + c in the equivalent form a(x - h)^2 + k. Because a squared bracket is never negative, the constant k is the minimum value of the function when a is positive and the maximum value when a is negative, attained at x = h; the point (h, k) is therefore the turning point of the parabola. The rearrangement changes only how the expression is written, never its value at any x.
This definition is part of the Quadratic Functions chapter in Cambridge IGCSE Additional Mathematics.