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4024/22 May/Jun 2026, Question 25: Completing the square

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 5 marks

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The question, in short

Work with the quadratic 2x² − 8x + 7 by completing the square.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 3 marks

Write 2x² − 8x + 7 as a(x − b)² + c.

  1. 12x² − 8x + 7 = 2(x² − 4x) + 7
  2. 2= 2[(x − 2)² − 4] + 7
  3. 3= 2(x − 2)² − 8 + 7
  4. 4= 2(x − 2)² − 1

Answer2(x − 2)² − 1

Part (b) · 1 mark

Give the turning point of y = 2x² − 8x + 7.

  1. 1Minimum when x − 2 = 0
  2. 2Turning point (2, −1)

Answer(2, −1)

Part (c) · 1 mark

2x² − 8x + 7 = k has two solutions. Complete k > ….

  1. 1The minimum value of y is −1
  2. 2The line y = k meets the curve twice when k > −1

Answer−1

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

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Also searched as: 4024/22/M/J/26 · 4024_s26_qp_22 · 4024 s26 22 · question 25.
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