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0580/32 Oct/Nov 2023, Question 4: Quadratic Graphs and the Parabola

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 8 marks

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The question, in short

For y = x² − 4x − 2, fill in missing table values, plot the curve for −2 ≤ x ≤ 5, and use the graph to solve x² − 4x − 2 = 0.

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

Part (a) · 2 marks

Complete the table by finding the missing y-values for y = x² − 4x − 2 at the given x-values.

  1. 1x = −2: (−2)² − 4 × (−2) − 2 = 4 + 8 − 2 = 10
  2. 2x = 2: 2² − 4 × 2 − 2 = 4 − 8 − 2 = −6

Answer| x | −2 | 2 | | y | 10 | −6 |

Part (b) · 4 marks

Draw the graph of y = x² − 4x − 2 on the grid for x from −2 to 5.

  1. 1Plot (−2, 10), (−1, 3), (0, −2), (1, −5), (2, −6), (3, −5), (4, −2), (5, 3)
  2. 2Join with a smooth U-shaped curve, lowest point at (2, −6)

AnswerCorrect curve

Part (c) · 2 marks

Use your drawn graph to find the solutions of x² − 4x − 2 = 0.

  1. 1Read where the curve crosses y = 0 (the x-axis)
  2. 2x ≈ −0.4 and x ≈ 4.4 (exactly 2 ± √6)

Answer−0.6 to −0.3, 4.3 to 4.6

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Also searched as: 0580/32/O/N/23 · 0580_w23_qp_32 · 0580 w23 32 · question 4.
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