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0580/33 Oct/Nov 2024, Question 8: Quadratic Graphs and the Parabola

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 11 marks

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The question, in short

Complete a table for y = 4x − x², plot its graph for −1 ≤ x ≤ 6, use the graph to solve 4x − x² = 1, and find the equation of line L shown on a grid.

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 = 4x − x² at x = 4 and x = 6.

  1. 1x = 4: 16 − 16 = 0
  2. 2x = 6: 24 − 36 = −12

Answer| x | 4 | 6 | | y | 0 | −12 |

Part (aii) · 4 marks

Draw the curve y = 4x − x² on the grid for x from −1 to 6.

  1. 1Plot (−1, −5), (0, 0), (1, 3), (2, 4), (3, 3), (4, 0), (5, −5), (6, −12)
  2. 2Join with a smooth ∩-shaped curve

AnswerCorrect curve

Part (aiii) · 2 marks

Using your drawn graph, find the x-values where 4x − x² equals 1.

  1. 1Draw the line y = 1 and read x where it meets the curve
  2. 2x² − 4x + 1 = 0 gives x = 2 ± √3
  3. 3x ≈ 0.3 and x ≈ 3.7

Answer0.2 to 0.4, 3.6 to 3.8

Part (b) · 3 marks

Find the equation of the straight line L shown on the grid.

  1. 1Gradient = (5 − (−4))/(4 − (−2)) = 9/6 = 1.5
  2. 2y-intercept = −1
  3. 3y = 1.5x − 1

Answery = 1.5x − 1

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Also searched as: 0580/33/O/N/24 · 0580_w24_qp_33 · 0580 w24 33 · question 8.
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