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AlgebraStudy Notes

Worked Example 1

Part of Completing the Square — GCSE Mathematics

This study notes covers Worked Example 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 3 of 5 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 3 of 5

Practice

10 questions

Recall

3 flashcards

Worked Example 1

Write x² + 8x + 5 in the form (x + p)² + q

Step 1 Find p

p = half of 8 = 4

Step 2 Write in form

(x + 4)² − 4² + 5

= (x + 4)² − 16 + 5

= (x + 4)² − 11

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 2: Negative bA Perfect FormWorked 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 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

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Worked Example 2: Negative b