AlgebraDeep Dive

Method: When a = 1

Part of Completing the Square · GCSE GCSE Mathematics revision

This deep dive covers Method: When a = 1 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 2 of 6 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 2 of 6

Practice

10 questions

Recall

3 flashcards

Method: When a = 1

To write x² + bx + c in the form (x + p)² + q:

1 p = half of b (the coefficient of x)

2 Write (x + p)² − p² + c

3 Simplify to get (x + p)² + q

Key insight: (x + p)² + q has turning point at (−p, q)

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.

A Perfect Form Worked Example 1 Worked Example 2: Negative b Worked Example 3: Finding Turning Point

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 Square Formula

x² + bx + c = (x + b/2)² − (b/2)² + c. Halve b, square it, adjust constant.

Completing the Square

(x + p)² + q form. Half the b term, square it

10 questions on Completing the Square — practise free

Instant marking, adaptive difficulty, and 3 spaced repetition flashcards. Free until your GCSEs.

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A Perfect Form

Worked Example 1