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4MA1/1HR Jun 2025, Question 21: Transformations of Graphs

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 3 marks

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The question, in short

A curve y = f(x) has a single turning point at (−6, 9). Find the turning point after a horizontal transformation, and find a and b for a translated curve mapping (4, −5) to (1, −16).

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Part (a) · 1 mark

State the coordinates of the turning point of y = f(3x), given the original turning point is (−6, 9).

  1. 1y = f(3x) is a stretch parallel to the x-axis, scale factor 1/3
  2. 2x-coordinate: −6 ÷ 3 = −2, y unchanged
  3. 3(−2, 9)

Answer(−2, 9)

Part (b) · 2 marks

Given (4, −5) on y = g(x) maps to (1, −16) on y = g(x + a) + b, state a and b.

  1. 1y = g(x + a) + b is a translation by (−a, b)
  2. 2x: 4 − a = 1, so a = 3
  3. 3y: −5 + b = −16, so b = −11

Answera = 3, b = −11

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