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0580/31 May/Jun 2024, Question 8: Quadratic Graphs and the Parabola

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 10 marks

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The question, in short

Table of values for y = x² − x − 3 from x = −3 to 4; complete it, plot the curve, identify the minimum point, and solve x² − x − 3 = 7 graphically.

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

Part (a) · 3 marks

Fill in the missing y-values in the table for y = x² − x − 3 at the given x-values.

  1. 1x = −3: 9 + 3 − 3 = 9
  2. 2x = −2: 4 + 2 − 3 = 3
  3. 3x = 0: −3; x = 1: 1 − 1 − 3 = −3
  4. 4x = 3: 9 − 3 − 3 = 3

Answer9, 3, −3, −3, 3

Part (b) · 4 marks

Plot the graph of y = x² − x − 3 on the grid for −3 ≤ x ≤ 4.

  1. 1Plot the 8 points from the table
  2. 2(−3, 9), (−2, 3), (−1, −1), (0, −3), (1, −3), (2, −1), (3, 3), (4, 9)
  3. 3Join with a smooth U-shaped curve, lowest at x = 0.5

AnswerCompletely correct curve through (−3, 9), (−2, 3), (−1, −1), (0, −3), (1, −3), (2, −1), (3, 3), (4, 9)

Part (c) · 1 mark

Sketch the curve and state the coordinates of its lowest point.

  1. 1Curve is symmetrical about x = 0.5 (halfway between 0 and 1)
  2. 2y at x = 0.5 ≈ −3.25
  3. 3Lowest point (0.5, −3.25)

Answer(0.4 to 0.6, −3.6 to −3)

Part (d) · 2 marks

Using your graph, find the x-values where x² − x − 3 equals 7.

  1. 1Draw the line y = 7 on the grid
  2. 2Read off x where the curve meets y = 7
  3. 3x = −2.7 or x = 3.7

Answerx = −2.8 to −2.6 or x = 3.6 to 3.8

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Also searched as: 0580/31/M/J/24 · 0580_s24_qp_31 · 0580 s24 31 · question 8.
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