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4MA1/1H Jan 2022, Question 20: The Quadratic Formula and Completing the Square

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 4 marks

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The question, in short

Rewrite the quadratic 7 + 12x − 3x² in completed-square form with integer a, b, c, then use it to find the maximum point A of the curve y = 7 + 12x − 3x².

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

Part (a) · 3 marks

Complete the square on 7 + 12x − 3x², giving integers a, b and c in the form a + b(x + c)².

  1. 1Take out −3: 7 − 3(x² − 4x)
  2. 2Complete the square: x² − 4x = (x − 2)² − 4
  3. 37 − 3[(x − 2)² − 4] = 7 − 3(x − 2)² + 12
  4. 419 − 3(x − 2)²

Answer19 − 3(x − 2)²

Part (b) · 1 mark

Read off the coordinates of the maximum point A of the curve from the completed-square result.

  1. 1From part (a), y = 19 − 3(x − 2)²
  2. 2(x − 2)² is never negative, so y is largest when x = 2
  3. 3Then y = 19, so A is (2, 19)

Answer(2, 19)

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