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0580/33 May/Jun 2021, Question 9: Quadratic Graphs and the Parabola

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 9 marks

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The question, in short

Table of values for y = x² + x − 5 with some y entries missing; find the missing values, plot the curve from x = −4 to 3, state its symmetry line, and use the curve to solve x² + x − 5 = 0.

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

Part (a) · 2 marks

Work out the y-values that are blank in the table for the given x-values.

  1. 1x = −3: (−3)² + (−3) − 5 = 9 − 3 − 5 = 1
  2. 2x = 1: 1 + 1 − 5 = −3
  3. 3x = 2: 4 + 2 − 5 = 1

Answer| x | −3 | 1 | 2 | | y | 1 | −3 | 1 |

Part (b) · 4 marks

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

  1. 1Plot (−4, 7), (−3, 1), (−2, −3), (−1, −5), (0, −5), (1, −3), (2, 1), (3, 7)
  2. 2Join with a smooth U-shaped curve (lowest point just below −5 at x = −0.5)

AnswerCorrect curve

Part (c) · 1 mark

State the equation of the mirror line of the plotted curve.

  1. 1y = −5 at both x = −1 and x = 0, so the curve is symmetric halfway between
  2. 2x = −0.5

Answerx = −0.5

Part (d) · 2 marks

From your curve, find the x-values where y equals zero.

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

Answer−2.9 to −2.7 and 1.7 to 1.9

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Also searched as: 0580/33/M/J/21 · 0580_s21_qp_33 · 0580 s21 33 · question 9.
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