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4024/21 Oct/Nov 2024, Question 3: Quadratic Graphs and the Parabola

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 9 marks

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The question, in short

Use the quadratic y = 4 + 2x − x²/2: fill missing table values, plot its curve for −2 ≤ x ≤ 6, state its symmetry line, add the straight line 3y = x + 6, and give x-values where the two graphs meet.

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

Part (a) · 2 marks

Work out the two missing y-values in the table for y = 4 + 2x − x²/2 at x = −2 and x = 6.

  1. 1x = −2: y = 4 + 2(−2) − (−2)²/2 = 4 − 4 − 2 = −2
  2. 2x = 6: y = 4 + 12 − 36/2 = −2

Answer| x | −2 | 6 | | y | −2 | −2 |

Part (b) · 3 marks

Plot the curve y = 4 + 2x − x²/2 on the grid across the range −2 ≤ x ≤ 6.

  1. 1Plot (−2, −2), (−1, 1.5), (0, 4), (1, 5.5), (2, 6), (3, 5.5), (4, 4), (5, 1.5), (6, −2)
  2. 2Join with a smooth curve, maximum at (2, 6)

AnswerCorrect smooth curve

Part (c) · 1 mark

Give the equation of the mirror line about which the plotted curve is symmetric.

  1. 1The curve is symmetrical about its maximum point (2, 6)
  2. 2x = 2

Answerx = 2

Part (d) · 2 marks

Plot the straight line 3y = x + 6 on the same grid between x = −2 and x = 6.

  1. 13y = x + 6 gives y = x/3 + 2
  2. 2Plot (0, 2), (3, 3) and (6, 4) and rule a straight line from x = −2 to x = 6

AnswerCorrect ruled line

Part (e) · 1 mark

State the x-coordinates where the curve and the straight line cross.

  1. 1Read the x-coordinates where the line crosses the curve
  2. 2Check: 4 + 2x − x²/2 = (x + 6)/3 gives 3x² − 10x − 12 = 0
  3. 3x ≈ −0.9 and x ≈ 4.3

Answer−1.05 to −0.85, 4.15 to 4.35

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Also searched as: 4024/21/O/N/24 · 4024_w24_qp_21 · 4024 w24 21 · question 3.
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