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AlgebraIntroduction

A Perfect Form

Part of Completing the Square — GCSE Mathematics

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 5 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 1 of 5

Practice

10 questions

Recall

3 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.
Completing the square diagram

Keep building this topic

Read this section alongside the surrounding pages in Completing the Square. That gives you the full topic sequence instead of a single isolated revision point.

Method: When a = 1Worked Example 1Worked Example 2: Negative b

Practice Questions for Completing the Square

To write x² + 10x + 3 in the form (x + p)² + q, what is the value of p?

  • A. 10
  • B. 5
  • C. 3
  • D. 25
1 markfoundation

Explain how you can tell from the completed square form whether a quadratic has a minimum or a maximum turning point.

2 markshigher

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.

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Method: When a = 1