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0580/32 Oct/Nov 2021, Question 10: Quadratic Graphs and the Parabola

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 9 marks

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The question, in short

For y = x² − 5x − 2, complete a table of values, plot the curve for −2 ≤ x ≤ 6, add the line y = 2, and use the graph to solve x² − 5x − 2 = 2.

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 = x² − 5x − 2 at the given x values.

  1. 1x = −2: y = 4 + 10 − 2 = 12
  2. 2x = 1: y = 1 − 5 − 2 = −6
  3. 3x = 4: y = 16 − 20 − 2 = −6

Answer12, −6, −6

Part (b) · 4 marks

Plot the graph of y = x² − 5x − 2 on the grid for x from −2 to 6.

  1. 1Plot (−2, 12), (−1, 4), (0, −2), (1, −6), (2, −8), (3, −8), (4, −6), (5, −2), (6, 4)
  2. 2Join with a smooth U-shaped curve (minimum between x = 2 and x = 3)

AnswerCorrect curve

Part (c) · 1 mark

Draw the horizontal line y = 2 on the same grid.

  1. 1Rule a horizontal line through y = 2 across the grid

AnswerRuled line y = 2 drawn

Part (d) · 2 marks

Using your graph, find the x values where x² − 5x − 2 equals 2.

  1. 1Read the x-values where the curve crosses y = 2
  2. 2Check: x² − 5x − 4 = 0 gives x = (5 ± √41)/2
  3. 3x ≈ −0.7 and x ≈ 5.7

Answer−0.9 to −0.5 and 5.5 to 5.9

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Also searched as: 0580/32/O/N/21 · 0580_w21_qp_32 · 0580 w21 32 · question 10.
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