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0580/31 Oct/Nov 2021, Question 10: Quadratic Graphs and the Parabola

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 8 marks

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The question, in short

Complete a table for y = 4 + 3x − x², plot its graph for −2 ≤ x ≤ 4, then use the graph with the line y = 2x − 1 to solve 4 + 3x − x² = 2x − 1.

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

Part (a) · 2 marks

Fill in the missing y values in the table for y = 4 + 3x − x² at the given x values.

  1. 1x = −2: y = 4 − 6 − 4 = −6
  2. 2x = 1: y = 4 + 3 − 1 = 6
  3. 3x = 3: y = 4 + 9 − 9 = 4

Answer−6, 6, 4

Part (b) · 4 marks

Draw the curve y = 4 + 3x − x² on the grid for x from −2 to 4.

  1. 1Plot (−2, −6), (−1, 0), (0, 4), (1, 6), (2, 6), (3, 4), (4, 0)
  2. 2Join with a smooth curve (maximum just above 6 at x = 1.5)

AnswerCorrect curve

Part (c) · 2 marks

Using your graph and the drawn line y = 2x − 1, find the x values solving 4 + 3x − x² = 2x − 1.

  1. 1Read the x-values where the curve crosses y = 2x − 1
  2. 2Check: x² − x − 5 = 0 gives x = (1 ± √21)/2
  3. 3x ≈ 2.8 and x ≈ −1.8

Answer2.7 to 2.9 and −1.9 to −1.7

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Also searched as: 0580/31/O/N/21 · 0580_w21_qp_31 · 0580 w21 31 · question 10.
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