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4MA1/1HR Jun 2023, Question 20: Transformations of Graphs

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 7 marks

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The question, in short

Curve C has a maximum at (3, 5). Find the maximum coordinates after three transformations, then find the equation of curve S obtained by translating y = x² + 7x + 20 by vector (2, 0).

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

Part (ai) · 1 mark

State the coordinates of the maximum point of y = 2f(x).

  1. 1The transformation y = 2f(x) scales the y-values by a factor of 2.
  2. 2The original maximum point is (3, 5).
  3. 3So the new y-coordinate is 2 × 5 = 10.
  4. 4The x-coordinate remains unchanged: 3.
  5. 5(3, 10)

Answer(3, 10)

Part (aii) · 1 mark

State the coordinates of the maximum point of y = f(x) − 7.

  1. 1The transformation y = f(x) − 7 shifts the graph down by 7 units.
  2. 2The original maximum point is (3, 5).
  3. 3So the new y-coordinate is 5 − 7 = −2.
  4. 4The x-coordinate remains unchanged: 3.
  5. 5(3, −2)

Answer(3, −2)

Part (aiii) · 1 mark

State the coordinates of the maximum point of y = f(−x).

  1. 1The transformation y = f(−x) reflects the graph in the y-axis.
  2. 2The original maximum point is (3, 5).
  3. 3So the new x-coordinate is −3.
  4. 4The y-coordinate remains unchanged: 5.
  5. 5(−3, 5)

Answer(−3, 5)

Part (b) · 4 marks

Find the equation of S after translating curve L by vector (2, 0), giving it as y = ax² + bx + c.

  1. 1Curve L: y = x² + 7x + 20.
  2. 2Translation vector is (2, 0), meaning a shift 2 units to the right.
  3. 3To translate right by 2, replace x with (x − 2).
  4. 4Substitute (x − 2) into the equation:
  5. 5(x − 2)² + 7(x − 2) + 20
  6. 6Expand: (x² − 4x + 4) + (7x − 14) + 20
  7. 7Combine like terms: x² − 4x + 4 + 7x − 14 + 20
  8. 8x² + 3x + 10
  9. 9y = x² + 3x + 10

Answery = x² + 3x + 10

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