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4MA1/2H Jun 2025, Question 25: The Quadratic Formula and Completing the Square

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks

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The question, in short

Rewrite 28 + 24x − 6x² as a − b(x − c)² with integer a, b, c, then sketch y = 28 + 24x − 6x² showing the turning point and y-axis intercept.

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

Part (a) · 3 marks

Express 28 + 24x − 6x² in the completed-square form a − b(x − c)², giving integer values of a, b and c.

  1. 128 + 24x − 6x² = 28 − 6(x² − 4x)
  2. 2x² − 4x = (x − 2)² − 4
  3. 328 − 6[(x − 2)² − 4] = 28 + 24 − 6(x − 2)²
  4. 4= 52 − 6(x − 2)²
  5. 5a = 52, b = 6, c = 2

Answer52 − 6(x − 2)²

Part (b) · 3 marks

Sketch the quadratic curve on the axes, marking clearly the turning point coordinates and where it crosses the y-axis.

  1. 1From (a), maximum turning point at (2, 52)
  2. 2Negative x² term, so the curve is ∩-shaped
  3. 3When x = 0, y = 28, so it crosses the y-axis at (0, 28)
  4. 4Draw a symmetrical ∩ curve through (0, 28) with its top at (2, 52)

AnswerA ∩-shaped parabola with maximum turning point at (2, 52), crossing the y-axis at (0, 28)

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