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0580/32 Feb/Mar 2022, Question 8: Quadratic Graphs and the Parabola

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 13 marks

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The question, in short

For y = x² + 6x − 160, fill in missing table values, plot the curve on the given grid, identify its symmetry line and minimum point, sketch it, and solve x² + 6x − 160 = 0; also rearrange y = mx + c for x.

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

Part (ai) · 3 marks

Work out the three missing y-values in the table for y = x² + 6x − 160 at x = −15, 10 and 15.

  1. 1x = −15: 225 − 90 − 160 = −25
  2. 2x = 10: 100 + 60 − 160 = 0
  3. 3x = 15: 225 + 90 − 160 = 155

Answer| x | −15 | 10 | 15 | | y | −25 | 0 | 155 |

Part (aii) · 4 marks

Plot the curve y = x² + 6x − 160 on the grid for x from −20 to 15.

  1. 1Plot (−20, 120), (−15, −25), (−10, −120), (−5, −165), (0, −160), (5, −105), (10, 0), (15, 155)
  2. 2Join with a smooth U-shaped curve, lowest near x = −3

AnswerCompletely correct curve

Part (aiiia) · 1 mark

  1. 1The curve is symmetric midway between x = −5 and x = −1 (equal y-values)
  2. 2x = −3

Answerx = −3

Part (aiiib) · 1 mark

Give the coordinates of the minimum point of the curve.

  1. 1At x = −3: y = 9 − 18 − 160 = −169
  2. 2Lowest point = (−3, −169)

Answer(−3, −180 to −165)

Part (aiv) · 2 marks

Draw a sketch of the curve and use it to find the solutions of x² + 6x − 160 = 0.

  1. 1Read where the curve crosses the x-axis (y = 0)
  2. 2x = −16 or x = 10

Answerx = 9.5 to 10.5 or x = −16.5 to −15.5

Part (b) · 2 marks

Make x the subject of y = mx + c.

  1. 1y − c = mx
  2. 2x = (y − c)/m

Answer(y − c)/m

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Also searched as: 0580/32/F/M/22 · 0580_m22_qp_32 · 0580 m22 32 · question 8.
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