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0580/33 Oct/Nov 2023, Question 10: Quadratic Graphs and the Parabola

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 4 marks

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The question, in short

Using the sketched parabola y = x² − 2x − 3 with x-intercepts at (−1, 0) and (3, 0), determine its axis of symmetry, verify a point, find another x for the same y, and state the y-intercept.

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

Part (a) · 1 mark

Determine the vertical line about which the parabola is symmetric.

  1. 1The line of symmetry is halfway between x = −1 and x = 3
  2. 2x = (−1 + 3)/2 = 1, so the line is x = 1

Answerx = 1

Part (bi) · 1 mark

Confirm that substituting x = 6 into the equation gives y = 21 for point A.

  1. 1k = 6² − 2 × 6 − 3
  2. 2= 36 − 12 − 3 = 21

Answer6² − 2 × 6 − 3 leading to 21

Part (bii) · 1 mark

Given B = (p, 21) on the curve, work out the unknown x-value p.

  1. 1p² − 2p − 3 = 21, so p² − 2p − 24 = 0
  2. 2(p − 6)(p + 4) = 0
  3. 3p = 6 is point A, so p = −4

Answer−4

Part (c) · 1 mark

State the y-value where the curve meets the vertical axis.

  1. 1At the y-axis x = 0: y = 0² − 2 × 0 − 3 = −3

Answer−3

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