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4MA1/2HR Jun 2018, Question 24: The Quadratic Formula and Completing the Square

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 6 marks

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The question, in short

Complete the square for 7 − 4x − x², use it to solve a related quadratic in y + 3 giving e ± √f, and state the maximum point of y = 3 − 5(x + 1)².

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

Part (a) · 2 marks

Rewrite 7 − 4x − x² as p − (x + q)², stating constants p and q.

  1. 1Write as 7 − (x² + 4x)
  2. 2Complete the square: x² + 4x = (x + 2)² − 4
  3. 37 − ((x + 2)² − 4) = 11 − (x + 2)²

Answer11 − (x + 2)²

Part (b) · 3 marks

Using part (a), solve 7 − 4(y + 3) − (y + 3)² = 0, giving answers as e ± √f with integers e, f.

  1. 1The equation is part (a) with x = y + 3, so 11 − (y + 5)² = 0
  2. 2(y + 5)² = 11, so y + 5 = ±√11
  3. 3y = −5 ± √11

Answer−5 ± √11

Part (c) · 1 mark

Give the coordinates of the maximum point A on the curve y = 3 − 5(x + 1)².

  1. 15(x + 1)² is never negative, so y is largest when x + 1 = 0
  2. 2x = −1 gives y = 3 − 0 = 3
  3. 3Maximum point A = (−1, 3)

Answer(−1, 3)

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