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0606/22 May/Jun 2026, Question 1: Completed Square Form and Turning Points

Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 4 marks

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The question, in short

For the curve y = x² − 6x + 10, locate its lowest point A by completing the square, then use points B (6, 7) and C on the y-axis to build a parallel line.

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Part (a) · 2 marks

Rewrite the quadratic by completing the square and state the coordinates of the minimum point A.

  1. 1y = (x − 3)² − 9 + 10
  2. 2y = (x − 3)² + 1
  3. 3Minimum when x − 3 = 0: A = (3, 1)

Answer(3, 1)

Part (b) · 2 marks

Find where the curve meets the y-axis, then give the equation of the line through B (6, 7) with the same gradient as AC.

  1. 1C = (0, 10)
  2. 2Gradient AC = (10 − 1)/(0 − 3) = −3
  3. 3Line through B(6, 7): y − 7 = −3(x − 6)
  4. 4y = 25 − 3x

Answery − 7 = −3(x − 6) (y = 25 − 3x)

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Also searched as: 0606/22/M/J/26 · 0606_s26_qp_22 · 0606 s26 22 · question 1.
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