This introduction covers A Perfect Form within Completing the Square for GCSE Mathematics. Revise Completing the Square in Algebra for GCSE Mathematics with 10 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 1 of 6 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.
A Perfect Form
x² + 6x + 9 = (x + 3)². That's a "perfect square". But what about x² + 6x + 5? It's not perfect... yet! Completing the square lets us rewrite ANY quadratic in a perfect form, revealing the turning point of its graph.
Practice questions for Completing the Square
To write x² + 10x + 3 in the form (x + p)² + q, what is the value of p?
Explain how you can tell from the completed square form whether a quadratic has a minimum or a maximum turning point.
Quick recall flashcards
Completing the Square
(x + p)² + q form. Half the b term, square it
Completing Square Formula
x² + bx + c = (x + b/2)² − (b/2)² + c. Halve b, square it, adjust constant.