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4MA1/2HR Jan 2019, Question 20: The Quadratic Formula and Completing the Square

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

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The question, in short

Express the quadratic 3x² − 12x + 7 in completed-square form a(x + b)² + c, then determine the equation of the vertical mirror line L of its graph.

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

Part (a) · 3 marks

Rewrite 3x² − 12x + 7 as a(x + b)² + c, giving the values of a, b and c.

  1. 1Take out 3 from the x terms: 3(x² − 4x) + 7
  2. 2Complete the square: x² − 4x = (x − 2)² − 4
  3. 33((x − 2)² − 4) + 7 = 3(x − 2)² − 12 + 7
  4. 4So the answer is 3(x − 2)² − 5

Answer3(x − 2)² − 5

Part (b) · 1 mark

Find the equation of the line of symmetry L of y = 3x² − 12x + 7, using part (a) if helpful.

  1. 1x = 2

Answerx = 2

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