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WMA11/01 Oct 2023, Question 11: Completed Square Form and Turning Points

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 10 marks

The question, in short

For the curve y = 2x² − 12x + 14, complete the square, find its minimum point P, find the line through (−1, 28) and P, and describe region R with inequalities.

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

Part (a) · 3 marks

Rewrite 2x² − 12x + 14 as a(x + b)² + c, finding constants a, b and c.

  1. 1Take out 2: 2(x² − 6x) + 14
  2. 2Complete the square: 2[(x − 3)² − 9] + 14
  3. 3= 2(x − 3)² − 4

Answer2(x − 3)² − 4

Part (b) · 1 mark

Give the coordinates of the minimum point P of the curve.

  1. 1Minimum when x − 3 = 0
  2. 2P = (3, −4)

AnswerP(3, −4)

Part (c) · 3 marks

Find the equation of line l through (−1, 28) and P in y = mx + c form.

  1. 1Gradient = (28 − (−4))/(−1 − 3) = 32/(−4) = −8
  2. 2y − 28 = −8(x + 1)
  3. 3y = −8x + 20

Answery = −8x + 20

Part (d) · 3 marks

Write inequalities defining region R bounded by the x-axis, y-axis, line l and curve C.

  1. 1R is below the line l: y ≤ −8x + 20
  2. 2R is above the curve C: y ≥ 2x² − 12x + 14
  3. 3R is above the x-axis and right of the y-axis: y ≥ 0, x ≥ 0

Answery ≤ −8x + 20, y ≥ 2x² − 12x + 14, y ≥ 0, x ≥ 0 (strict < and > also accepted, used consistently)

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