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4PM1/01 Jun 2019, Question 5: The Quadratic Formula and Completing the Square

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 5 marks

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The question, in short

A quadratic f(x) = 3x² − 9x + 5 is to be rewritten as a(x − b)² + c, then its least value and where that least value happens are required.

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Part (a) · 3 marks

Complete the square on 3x² − 9x + 5 and state the constants a, b and c.

  1. 1f(x) = 3(x² − 3x) + 5
  2. 2= 3[(x − 3/2)² − 9/4] + 5
  3. 3= 3(x − 3/2)² − 27/4 + 5 = 3(x − 3/2)² − 7/4
  4. 4a = 3, b = 3/2, c = −7/4

Answera = 3, b = 3/2, c = −7/4

Part (b) · 2 marks

Using your completed-square form, give the smallest value of f(x) and the x-value producing it.

  1. 1Minimum value of f(x) = c = −7/4
  2. 2It occurs when x − 3/2 = 0, so x = 3/2

Answer(i) −7/4 (ii) x = 3/2

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