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0580/32 Oct/Nov 2024, Question 8: Quadratic Graphs and the Parabola

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 15 marks

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The question, in short

Using a grid with line L from (0, 2) to (8, 6), work with y = 8 − 2x and y = x² − 4x − 4, finding equations, tables, graphs, symmetry and solutions.

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

Part (ai) · 2 marks

Work out the equation of L in the form y = mx + c.

  1. 1Gradient = (6 − 2)/(8 − 0) = 1/2
  2. 2y-intercept = 2
  3. 3y = (1/2)x + 2

Answery = (1/2)x + 2

Part (aiia) · 2 marks

Fill the missing y-values in the table for y = 8 − 2x at x = 0 and x = 4.

  1. 1x = 0: y = 8 − 0 = 8
  2. 2x = 4: y = 8 − 8 = 0

Answer| x | 0 | 2 | 4 | | y | 8 | 4 | 0 |

Part (aiib) · 1 mark

Plot y = 8 − 2x on the grid between x = 0 and x = 4.

  1. 1Plot (0, 8), (2, 4), (4, 0) and join with a ruled line

AnswerCorrect graph

Part (aiii) · 1 mark

State the coordinates where L meets y = 8 − 2x.

  1. 1(1/2)x + 2 = 8 − 2x
  2. 22.5x = 6, x = 2.4
  3. 3y = 8 − 4.8 = 3.2
  4. 4(2.4, 3.2)

Answer(2.4, 3.2)

Part (bi) · 2 marks

Fill the missing y-values in the table for y = x² − 4x − 4 at x = −1, 1, 3 and 5.

  1. 1x = −1: 1 + 4 − 4 = 1
  2. 2x = 1: 1 − 4 − 4 = −7
  3. 3x = 3: 9 − 12 − 4 = −7
  4. 4x = 5: 25 − 20 − 4 = 1

Answer| x | −1 | 1 | 3 | 5 | | y | 1 | −7 | −7 | 1 |

Part (bii) · 4 marks

Draw y = x² − 4x − 4 on the grid from x = −2 to x = 6.

  1. 1Plot (−2, 8), (−1, 1), (0, −4), (1, −7), (2, −8), (3, −7), (4, −4), (5, 1), (6, 8)
  2. 2Join with a smooth U-shaped curve

AnswerCorrect curve

Part (biii) · 1 mark

Give the equation of the mirror line of the curve.

  1. 1The curve is symmetrical about its lowest point, (2, −8)
  2. 2x = 2

Answerx = 2

Part (biv) · 2 marks

Use your graph to find the solutions of x² − 4x − 4 = 0.

  1. 1Read x where the curve crosses y = 0
  2. 2x = 2 ± √8: x ≈ −0.8 and x ≈ 4.8

Answer−0.7 to −0.9, 4.7 to 4.9

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Also searched as: 0580/32/O/N/24 · 0580_w24_qp_32 · 0580 w24 32 · question 8.
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