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0580/13 May/Jun 2026, Question 13: Quadratic Graphs and the Parabola

Cambridge IGCSE Mathematics 0580 · Paper 13 (Core) · Non-calculator · 9 marks

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The question, in short

Complete a table for y = 6x − x² − 4, plot its graph for 0 ≤ x ≤ 6, add the line y = 3, and use the graph to solve 6x − x² − 4 = 3.

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 = 6x − x² − 4 at the given x values.

  1. 1x = 0: y = 0 − 0 − 4 = −4
  2. 2x = 1: y = 6 − 1 − 4 = 1
  3. 3x = 2: y = 12 − 4 − 4 = 4

Answer−4, 1, 4

Part (b) · 4 marks

Plot the curve y = 6x − x² − 4 on the grid for x from 0 to 6.

  1. 1Plot (0, −4), (1, 1), (2, 4), (3, 5), (4, 4), (5, 1), (6, −4)
  2. 2Join with a smooth symmetrical curve, maximum at (3, 5)

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

Part (c) · 1 mark

Draw the horizontal line y = 3 on the same grid.

  1. 1Draw a horizontal straight line through y = 3 from x = 0 to x = 6

AnswerLine y = 3 drawn from x = 0 to x = 6

Part (d) · 2 marks

From the graph, find the x values where 6x − x² − 4 equals 3.

  1. 1Read the x-coordinates where the curve meets the line y = 3
  2. 2x ≈ 1.6 or x ≈ 4.4

Answer1.5 to 1.7, 4.3 to 4.5

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Also searched as: 0580/13/M/J/26 · 0580_s26_qp_13 · 0580 s26 13 · question 13.
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