4MA1/1H Jun 2022, Question 24: The Quadratic Formula and Completing the Square
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 4 marks
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The question, in short
Find a, b and c, each as expressions in q, so that q + 12x − qx² equals a − b(x − c)².
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Solution · 4 marks
- 1Rewrite: q + 12x − qx² = q − q(x² − 12x/q)
- 2Complete the square: x² − 12x/q = (x − 6/q)² − 36/q²
- 3So the expression is q + 36/q − q(x − 6/q)²
- 4a = 36/q + q, b = q, c = 6/q
Answera = 36/q + q, b = q, c = 6/q
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