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4MA1/1H Jan 2019, Question 18: Transformations of Graphs

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

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The question, in short

Use the given graph of y = f(x), a U-shaped curve with key points, to sketch a transformed graph and to find a constant in a second transformation.

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

Part (a) · 2 marks

Sketch y = f(1/2 x) on the grid, using the original curve's intercepts and minimum point to place the stretched graph.

  1. 1y = f(½x) is a stretch, scale factor 2, parallel to the x-axis: (x, y) → (2x, y)
  2. 2Minimum (1, −4) → (2, −4); roots (−1, 0) and (3, 0) → (−2, 0) and (6, 0)
  3. 3(0, −3) stays; (−2, 5) → (−4, 5), (2, −3) → (4, −3), (4, 5) → (8, 5)
  4. 4Draw a parabola through (−4, 5), (−2, 0), (0, −3), (2, −4), (4, −3), (6, 0), (8, 5)

AnswerA parabola through (−4, 5), (−2, 0), (0, −3), (2, −4), (4, −3), (6, 0), (8, 5)

Part (b) · 1 mark

From the second grid showing y = f(x + k), write down the value of k.

  1. 1y = f(x + k) moves the graph k to the left
  2. 2The minimum has moved from x = 1 to x = −2
  3. 3That is 3 to the left, so k = 3

Answer3

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