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0580/22 May/Jun 2026, Question 21: Completing the square

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 3 marks

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The question, in short

Write x² + 8x − 7 as (x + a)² + b, then give the turning point of y = x² + 8x − 7.

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Part (a) · 2 marks

Complete the square.

  1. 1x² + 8x = (x + 4)² − 16
  2. 2x² + 8x − 7 = (x + 4)² − 16 − 7
  3. 3= (x + 4)² − 23

Answer(x + 4)² − 23

Part (b) · 1 mark

State the turning point.

  1. 1y = (x + 4)² − 23 is least when x + 4 = 0
  2. 2Turning point (−4, −23)

Answer(−4, −23)

Stuck on a step? Read the free lesson: The Quadratic Formula and Completing the Square

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Also searched as: 0580/22/M/J/26 · 0580_s26_qp_22 · 0580 s26 22 · question 21.
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