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0580/12 May/Jun 2025, Question 14: Quadratic Graphs and the Parabola

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Non-calculator · 11 marks

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The question, in short

For y = (x + 3)(x − 2), complete a values table, plot the curve for −4 ≤ x ≤ 3, then use it to find the minimum point, symmetry line, and solve (x + 3)(x − 2) = 3.

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 = (x + 3)(x − 2) at the given x-values from −4 to 3.

  1. 1x = −3: 0 × (−5) = 0; x = −1: 2 × (−3) = −6; x = 0: 3 × (−2) = −6
  2. 2x = 2: 5 × 0 = 0; x = 3: 6 × 1 = 6
  3. 3y values: 6, 0, −4, −6, −6, −4, 0, 6

Answer| x | −4 | −3 | −2 | −1 | 0 | 1 | 2 | 3 | | y | 6 | 0 | −4 | −6 | −6 | −4 | 0 | 6 |

Part (b) · 4 marks

Plot the graph of y = (x + 3)(x − 2) on the grid for x from −4 to 3.

  1. 1Plot (−4, 6), (−3, 0), (−2, −4), (−1, −6), (0, −6), (1, −4), (2, 0), (3, 6)
  2. 2Join with a smooth U-shaped curve, lowest between x = −1 and x = 0

AnswerCorrect curve

Part (c) · 1 mark

From a sketch of the curve, state the coordinates of the lowest point.

  1. 1Lowest point at x = −0.5: y = 2.5 × (−2.5) = −6.25
  2. 2(−0.5, −6.25)

Answer(−0.5, −6.6 to −6)

Part (d) · 1 mark

From a sketch of the curve, state the equation of its line of symmetry.

  1. 1The curve is symmetric about the lowest point: x = −0.5

Answerx = −0.5

Part (e) · 2 marks

Using the graph, solve (x + 3)(x − 2) = 3.

  1. 1Draw y = 3 and read where it meets the curve
  2. 2Check: x² + x − 9 = 0 gives x = (−1 ± √37)/2
  3. 3x ≈ −3.54 and x ≈ 2.54

Answer−3.6 to −3.4, 2.4 to 2.6

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