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4MA1/2HR Jun 2019, Question 3: Quadratic Graphs and the Parabola

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

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The question, in short

Complete a table of values for y = 1 + 5x − x², then plot the graph of the curve for x from −1 to 6 on the given grid.

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

Part (a) · 2 marks

Fill in the missing y values in the table for y = 1 + 5x − x² at the given x values from −1 to 6.

  1. 1y = 1 + 5x − x²
  2. 2x = −1: y = 1 + 5(−1) − (−1)² = 1 − 5 - 1 = −5
  3. 3x = 1: y = 1 + 5(1) − 1² = 1 + 5 − 1 = 5
  4. 4x = 4: y = 1 + 5(4) − 4² = 1 + 20 − 16 = 5
  5. 5x = 6: y = 1 + 5(6) − 6² = 1 + 30 − 36 = −5
  6. 6Completed table for x = −1 to 6: y = −5, 1, 5, 7, 7, 5, 1, −5
  7. 7Plot (−1, −5), (0, 1), (1, 5), (2, 7), (3, 7), (4, 5), (5, 1), (6, −5)
  8. 8Join the points with a smooth curve to give the graph of y = 1 + 5x − x²

Answer−5, 5, 5, −5

Part (b) · 2 marks

Draw the curve y = 1 + 5x − x² on the grid for x values between −1 and 6.

  1. 1y = 1 + 5x − x²
  2. 2x = −1: y = 1 + 5(−1) − (−1)² = 1 − 5 - 1 = −5
  3. 3x = 1: y = 1 + 5(1) − 1² = 1 + 5 − 1 = 5
  4. 4x = 4: y = 1 + 5(4) − 4² = 1 + 20 − 16 = 5
  5. 5x = 6: y = 1 + 5(6) − 6² = 1 + 30 − 36 = −5
  6. 6Completed table for x = −1 to 6: y = −5, 1, 5, 7, 7, 5, 1, −5
  7. 7Plot (−1, −5), (0, 1), (1, 5), (2, 7), (3, 7), (4, 5), (5, 1), (6, −5)
  8. 8Join the points with a smooth curve to give the graph of y = 1 + 5x − x²

AnswerSmooth curve through (−1, −5), (0, 1), (1, 5), (2, 7), (3, 7), (4, 5), (5, 1), (6, −5)

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