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0580/32 Feb/Mar 2023, Question 6: Quadratic Graphs and the Parabola

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

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The question, in short

Using a given straight line L on a coordinate grid, work out its equation and intercept, complete and plot a quadratic, then solve the quadratic equal to 6 graphically.

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

Part (a) · 2 marks

Work out the equation of the drawn straight line L, giving it as y = mx + c.

  1. 1L crosses the y-axis at (0, 7), so c = 7
  2. 2L passes through (−2, 3): gradient = (7 − 3)/(0 − (−2)) = 4/2 = 2
  3. 3y = 2x + 7

Answery = 2x + 7

Part (b) · 1 mark

State the coordinates where line L meets the x-axis.

  1. 1On the x-axis y = 0: 2x + 7 = 0
  2. 2x = −3.5
  3. 3(−3.5, 0)

Answer(−3.5, 0)

Part (ci) · 3 marks

Fill in the missing y-values in the table for y = x² + 5x + 3 at the listed x-values.

  1. 1x = −5: 25 − 25 + 3 = 3
  2. 2x = −3: 9 − 15 + 3 = −3
  3. 3x = −2: 4 − 10 + 3 = −3
  4. 4x = 0: 0 + 0 + 3 = 3
  5. 5x = 1: 1 + 5 + 3 = 9
  6. 6Missing values: 3, −3, −3, 3, 9

Answer3, −3, −3, 3, 9

Part (cii) · 4 marks

Plot the curve y = x² + 5x + 3 on the grid for x from −6 to 1.

  1. 1Plot (−6, 9), (−5, 3), (−4, −1), (−3, −3), (−2, −3), (−1, −1), (0, 3), (1, 9)
  2. 2Join with a smooth U-shaped curve; the lowest point is at about (−2.5, −3.25)

AnswerCompletely correct curve

Part (di) · 1 mark

Add the horizontal line y = 6 to the grid.

  1. 1Draw a ruled horizontal line through y = 6 across the grid

AnswerCorrect ruled line drawn

Part (dii) · 2 marks

From where the curve and the line y = 6 meet, find the solutions of x² + 5x + 3 = 6.

  1. 1Read the x-values where the curve meets y = 6
  2. 2Check: x² + 5x − 3 = 0 gives x = (−5 ± √37)/2
  3. 3x ≈ 0.54 or x ≈ −5.54

Answer0.4 to 0.7, −5.7 to −5.4

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Also searched as: 0580/32/F/M/23 · 0580_m23_qp_32 · 0580 m23 32 · question 6.
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