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0580/23 May/Jun 2026, Question 26: The Quadratic Formula and Completing the Square

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 4 marks

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The question, in short

Express the quadratic 3x² − 6x + 5 in completed-square form a(x + b)² + c, then state the coordinates of the turning point of its graph.

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Part (a) · 3 marks

Rewrite 3x² − 6x + 5 as a(x + b)² + c, giving the values of a, b and c.

  1. 13x² − 6x + 5 = 3(x² − 2x) + 5
  2. 2= 3[(x − 1)² − 1] + 5
  3. 3= 3(x − 1)² − 3 + 5 = 3(x − 1)² + 2

Answer3(x − 1)² + 2

Part (b) · 1 mark

Give the coordinates of the turning point of y = 3x² − 6x + 5.

  1. 1Minimum when x − 1 = 0, so x = 1, y = 2
  2. 2(1, 2)

Answer(1, 2)

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Also searched as: 0580/23/M/J/26 · 0580_s26_qp_23 · 0580 s26 23 · question 26.
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