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0580/32 Feb/Mar 2021, Question 5: Quadratic Graphs and the Parabola

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 11 marks

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The question, in short

Complete a table for y = −x² − x + 14, plot its graph for −5 ≤ x ≤ 4, then use the graph to find symmetry, the maximum point, and solve −x² − x + 14 = −2.

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 + 14 at the given x-values.

  1. 1y = −x² − x + 14
  2. 2x = −5: −25 + 5 + 14 = −6; x = −4: −16 + 4 + 14 = 2
  3. 3x = −1: −1 + 1 + 14 = 14; x = 0: 14
  4. 4x = 3: −9 − 3 + 14 = 2; x = 4: −16 − 4 + 14 = −6
  5. 5y values: −6, 2, 8, 12, 14, 14, 12, 8, 2, −6

Answer| x | −5 | −4 | −3 | −2 | −1 | 0 | 1 | 2 | 3 | 4 | | y | −6 | 2 | 8 | 12 | 14 | 14 | 12 | 8 | 2 | −6 |

Part (b) · 4 marks

Draw the curve y = −x² − x + 14 on the grid for x from −5 to 4.

  1. 1Plot (−5, −6), (−4, 2), (−3, 8), (−2, 12), (−1, 14), (0, 14), (1, 12), (2, 8), (3, 2), (4, −6)
  2. 2Join with a smooth curve (an upside-down U) that peaks between x = −1 and x = 0

AnswerCompletely correct curve

Part (ci) · 1 mark

State the equation of the vertical line of symmetry of the sketched graph.

  1. 1The curve is symmetrical about the midpoint of x = −1 and x = 0
  2. 2x = −0.5

Answerx = −0.5

Part (cii) · 1 mark

Give the coordinates of the highest point (vertex) on the graph.

  1. 1Highest point is on x = −0.5
  2. 2y = −0.25 + 0.5 + 14 = 14.25
  3. 3(−0.5, 14.25)

Answer(−0.5, 14 to 14.8)

Part (d) · 2 marks

Use the drawn graph to find the x-values where −x² − x + 14 equals −2.

  1. 1Draw the line y = −2 on the grid
  2. 2Read off the x-values where it crosses the curve
  3. 3x ≈ −4.5 and x ≈ 3.5

Answer3.3 to 3.7, −4.7 to −4.3

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Also searched as: 0580/32/F/M/21 · 0580_m21_qp_32 · 0580 m21 32 · question 5.
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