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4MA1/1H Jun 2022, Question 20: Transformations of Graphs

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 2 marks

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The question, in short

A curve y = f(x) has a single maximum at (s, t). Find the maximum point coordinates for two transformed curves, giving answers in terms of s and t.

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

Part (i) · 1 mark

State the coordinates of the maximum of y = f(x − 2), in terms of s and t.

  1. 1The transformation y = f(x − 2) shifts the graph 2 units to the right.
  2. 2So the x-coordinate of the maximum point increases by 2.
  3. 3s becomes s + 2.
  4. 4The y-coordinate remains unchanged.
  5. 5t stays as t.
  6. 6(s + 2, t)

Answer(s + 2, t)

Part (ii) · 1 mark

State the coordinates of the maximum of y = 3f(x), in terms of s and t.

  1. 1The transformation y = 3f(x) stretches the graph vertically by a scale factor of 3.
  2. 2So the y-coordinate of the maximum point is multiplied by 3.
  3. 3t becomes 3t.
  4. 4The x-coordinate remains unchanged.
  5. 5s stays as s.
  6. 6(s, 3t)

Answer(s, 3t)

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