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4PM1/02 Jun 2021, Question 2: The Quadratic Formula and Completing the Square

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 6 marks

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The question, in short

A quadratic f(x) = 2 + (4/5)x − (1/25)x² is given; rewrite it as A − B(x + C)², then use that form to state the maximum of f(x) and where it occurs.

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

Part (a) · 4 marks

Express f(x) in the completed-square form A − B(x + C)² and state the constants A, B and C.

  1. 1f(x) = 2 − (1/25)(x² − 20x)
  2. 2= 2 − (1/25)[(x − 10)² − 100]
  3. 3= 6 − (1/25)(x − 10)²
  4. 4A = 6, B = 1/25, C = −10

AnswerA = 6, B = 1/25, C = −10

Part (b) · 2 marks

Using your completed-square form, write down the greatest value of f(x) and the x-value giving it.

  1. 1(x − 10)² ≥ 0, so the maximum of f(x) is A = 6
  2. 2It occurs when x − 10 = 0, x = 10

Answer(i) 6; (ii) x = 10

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