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4MA1/1HR Jan 2022, Question 20: Transformations of Graphs

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 6 marks

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The question, in short

Use a given turning point of y = f(x) to find transformed turning points, sketch a vertically stretched graph, and find values of a for a horizontally shifted graph.

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

Part (ai) · 1 mark

State the coordinates of the turning point after adding 5 to f(x).

  1. 1The turning point of y = f(x) is (−6, −4)
  2. 2For y = f(x) + 5, add 5 to the y-coordinate
  3. 3−4 + 5 = 1
  4. 4So the new turning point is (−6, 1)

Answer(−6, 1)

Part (aii) · 1 mark

State the coordinates of the turning point after replacing x with 3x.

  1. 1For y = f(3x), the x-values are scaled by a factor of 1/3
  2. 2Multiply the x-coordinate of the turning point by 1/3
  3. 3−6 × (1/3) = −2
  4. 4The y-coordinate remains unchanged
  5. 5So the new turning point is (−2, −4)

Answer(−2, −4)

Part (b) · 2 marks

Sketch y = 2g(x) for −1 ≤ x ≤ 7 using the given graph of g.

  1. 1The original points on y = g(x) are (−1, 3), (3, −1), (7, 3)
  2. 2For y = 2g(x), multiply all y-values by 2
  3. 3(−1, 3) becomes (−1, 6)
  4. 4(3, −1) becomes (3, −2)
  5. 5(7, 3) becomes (7, 6)
  6. 6Plot these points and join with straight lines forming a V shape with minimum at (3, −2)

AnswerA V shape through (−1, 6), (3, −2) and (7, 6), with its lowest point at (3, −2)

Part (c) · 2 marks

Given h(x) crosses the x-axis at (−1, 0) and (6, 0), find both values of a so h(x + a) passes through (2, 0).

  1. 1The roots of h(x) are x = −1 and x = 6
  2. 2So h(x + a) has roots when x + a = −1 or x + a = 6
  3. 3Given that h(x + a) passes through (2, 0), so x = 2 is a root
  4. 4Then 2 + a = −1 → a = −3
  5. 5Or 2 + a = 6 → a = 4
  6. 6The two possible values of a are −3 and 4

Answer−3, 4

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