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4MA1/2H Jan 2020, Question 21: Transformations of Graphs

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

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The question, in short

Use the maximum point (4, 6) on y = f(x) to find transformed maximum points, then find the equation of curve S after translating y = x² + 3x + 4 by vector (4, 6).

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 maximum point of y = f(x + 4), given the original maximum is (4, 6).

  1. 1The graph of y = f(x + 4) is a horizontal translation of y = f(x) by −4 units.
  2. 2The maximum point (4, 6) moves to (4 − 4, 6) = (0, 6).

Answer(0, 6)

Part (aii) · 1 mark

State the coordinates of the maximum point of y = f(2x), given the original maximum is (4, 6).

  1. 1The graph of y = f(2x) involves a horizontal stretch with scale factor 1/2.
  2. 2The x-coordinate of the maximum point becomes 4 × (1/2) = 2.
  3. 3The y-coordinate remains unchanged, so the point is (2, 6).

Answer(2, 6)

Part (b) · 2 marks

Find an equation for curve S, the image of y = x² + 3x + 4 under the translation with vector (4, 6); no simplification needed.

  1. 1The curve C: y = x² + 3x + 4 is translated by the vector (4, 6), meaning a shift of +4 in x and +6 in y.
  2. 2To apply the translation, replace x with (x − 4) and add 6 to the entire expression.
  3. 3So, y = (x − 4)² + 3(x − 4) + 4 + 6
  4. 4y = (x − 4)² + 3(x − 4) + 10

Answery = (x − 4)² + 3(x − 4) + 10

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