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0580/31 May/Jun 2025, Question 28: Quadratic Graphs and the Parabola

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 9 marks

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The question, in short

Complete a table for y = x² − x − 5, plot its graph for −3 ≤ x ≤ 4, then find the line of symmetry and use the graph to solve x² − x − 5 = 0.

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

Part (ai) · 2 marks

Fill in the missing y-values in the table for y = x² − x − 5 at the given x-values.

  1. 1x = −3: 9 + 3 − 5 = 7
  2. 2x = 0: 0 − 0 − 5 = −5
  3. 3x = 1: 1 − 1 − 5 = −5
  4. 4x = 4: 16 − 4 − 5 = 7

Answer7, [1], [−3], −5, −5, [−3], [1], 7

Part (aii) · 4 marks

Draw the curve y = x² − x − 5 on the grid for x from −3 to 4.

  1. 1Plot the 8 points from the table
  2. 2(−3, 7), (−2, 1), (−1, −3), (0, −5), (1, −5), (2, −3), (3, 1), (4, 7)
  3. 3Join with a smooth U-shaped curve, lowest point near (0.5, −5.25)

AnswerCorrect graph through (−3, 7), (−2, 1), (−1, −3), (0, −5), (1, −5), (2, −3), (3, 1), (4, 7)

Part (b) · 1 mark

State the equation of the vertical line of symmetry of the drawn graph.

  1. 1The curve is symmetric about the middle of x = 0 and x = 1
  2. 2x = 1/2

Answerx = 1/2

Part (c) · 2 marks

From the graph, find the x-values where x² − x − 5 equals 0.

  1. 1Read where the curve crosses the x-axis (y = 0)
  2. 2x = −1.8 or x = 2.8

Answer−1.9 to −1.7, 2.7 to 2.9

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Also searched as: 0580/31/M/J/25 · 0580_s25_qp_31 · 0580 s25 31 · question 28.
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