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0580/22 Oct/Nov 2022, Question 11: Recognising and Sketching Graph Shapes

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 3 marks

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The question, in short

Cubic graph y = (x − 3)(x + b)(x + 2) meets the y-axis at −30. Find b, then give the x-intercept that occurs when x > 0.

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Part (a) · 2 marks

Use the y-intercept value −30 to determine the constant b in the cubic expression.

  1. 1At the y-axis x = 0: (0 − 3)(0 + b)(0 + 2) = −30
  2. 2−6b = −30
  3. 3b = 5

Answer5

Part (b) · 1 mark

State the coordinates of the single x-axis crossing in the region x > 0.

  1. 1y = (x − 3)(x + 5)(x + 2) = 0 when x = 3, −5 or −2
  2. 2Only x = 3 is positive, so the point is (3, 0)

Answer(3, 0)

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Also searched as: 0580/22/O/N/22 · 0580_w22_qp_22 · 0580 w22 22 · question 11.
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