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4024/21 Oct/Nov 2025, Question 22: Completed Square Form and Turning Points

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 7 marks

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The question, in short

Sketch the straight line y = 2 − 3x, then complete the square on 2x² − 4x − 3 and sketch its curve with intercept and turning point labelled.

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

Part (a) · 1 mark

Draw the straight-line graph of y = 2 − 3x on the given axes.

  1. 1Straight line with negative gradient (−3) crossing the y-axis at 2
  2. 2It crosses the x-axis at x = 2/3

AnswerCorrect sketch

Part (bi) · 3 marks

Express 2x² − 4x − 3 in the completed-square form a(x − b)² + c.

  1. 12x² − 4x − 3 = 2(x² − 2x) − 3
  2. 2= 2[(x − 1)² − 1] − 3
  3. 3= 2(x − 1)² − 5

Answer2(x − 1)² − 5

Part (bii) · 3 marks

Sketch y = 2x² − 4x − 3, marking the y-intercept and the turning point coordinates.

  1. 1Positive U-shaped parabola
  2. 2y-intercept at x = 0: y = −3, label −3
  3. 3Turning point (minimum) at (1, −5), label it

AnswerCorrect sketch and (1, −5) and −3 marked

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Also searched as: 4024/21/O/N/25 · 4024_w25_qp_21 · 4024 w25 21 · question 22.
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