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4MA1/2HR Jun 2020, Question 24: The Quadratic Formula and Completing the Square

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks

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The question, in short

Rewrite the quadratic 7 + 12x − 3x² in completed-square form a + b(x + c)² with integer a, b, c, then use it to state the coordinates of the turning point A on curve C.

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

Part (a) · 4 marks

Express 7 + 12x − 3x² as a + b(x + c)², giving integers a, b and c.

  1. 1Start with the expression: 7 + 12x − 3x²
  2. 2Factor out −3 from the x terms: = −3(x² − 4x) + 7
  3. 3Complete the square inside the brackets: x² − 4x = (x − 2)² − 4
  4. 4Substitute back: −3[(x − 2)² − 4] + 7
  5. 5Expand: −3(x − 2)² + 12 + 7
  6. 6−3(x − 2)² + 19
  7. 7Rewrite as: 19 − 3(x − 2)²

Answer19 − 3(x − 2)²

Part (b) · 1 mark

From the completed-square form, write down the coordinates of the turning point A of the curve.

  1. 1From part (a), the equation is y = 19 − 3(x − 2)²
  2. 2This is a parabola in vertex form: y = a + b(x + c)²
  3. 3The turning point occurs at x = 2
  4. 4Substitute x = 2 into the expression: y = 19 − 3(0)² = 19
  5. 5So coordinates of A are (2, 19)

Answer(2, 19)

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