4MA1/1H Jun 2024, Question 25: 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
Given f(x) = 17 − 3x² + 12x, rewrite the expression as a − b(x − c)² and state the constants a, b and c.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 4 marks
- 1f(x) = 17 − 3x² + 12x
- 2Write the x terms first: f(x) = −3x² + 12x + 17
- 3Take out a factor of −3 from the x terms: f(x) = −3(x² − 4x) + 17
- 4Complete the square inside: x² − 4x = (x − 2)² − 4
- 5f(x) = −3[(x − 2)² − 4] + 17
- 6f(x) = −3(x − 2)² + 12 + 17
- 7f(x) = 29 − 3(x − 2)²
Answer29 − 3(x − 2)²
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