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0580/33 Oct/Nov 2021, Question 8: Quadratic Graphs and the Parabola

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 11 marks

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The question, in short

From a grid showing line L, find its equation as y = mx + c, then complete a table, plot y = x² + 4x, and use the graph to solve x² + 4x = 10.

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

Part (a) · 3 marks

Find the equation of line L shown on the grid, giving it in the form y = mx + c.

  1. 1Line L passes through (−4, 0) and (0, 10)
  2. 2Gradient = rise ÷ run = 10 ÷ 4 = 2.5
  3. 3y-intercept = 10
  4. 4y = 2.5x + 10

Answery = 2.5x + 10

Part (bi) · 2 marks

Fill in the two missing y-values in the table for y = x² + 4x at x = −2 and x = 3.

  1. 1x = −2: y = 4 − 8 = −4
  2. 2x = 3: y = 9 + 12 = 21

Answer−4, 21

Part (bii) · 4 marks

Plot the graph of y = x² + 4x on the grid for values of x from −6 to 3.

  1. 1Plot (−6, 12), (−5, 5), (−4, 0), (−3, −3), (−2, −4), (−1, −3), (0, 0), (1, 5), (2, 12), (3, 21)
  2. 2Join with a smooth U-shaped curve, minimum at (−2, −4)

AnswerCorrect curve

Part (biii) · 2 marks

Using your drawn graph, find the solutions to the equation x² + 4x = 10.

  1. 1Draw y = 10 and read the x-values where it crosses the curve
  2. 2Check: x² + 4x − 10 = 0 gives x = −2 ± √14
  3. 3x ≈ −5.7 and x ≈ 1.7

Answer−5.8 to −5.6 and 1.6 to 1.8

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Also searched as: 0580/33/O/N/21 · 0580_w21_qp_33 · 0580 w21 33 · question 8.
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