4MA1/2H Jun 2021, Question 22: Transformations of Graphs
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 4 marks
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The question, in short
Rewrite g(x) = 2x² − 12x + 13 as a(x − b)² − c, then describe fully the transformations taking y = x² onto y = g(x).
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 4 marks
- 1Complete the square: 2x² − 12x + 13 = 2(x² − 6x) + 13
- 2= 2[(x − 3)² − 9] + 13 = 2(x − 3)² − 5
- 3Multiplying x² by 2 is a stretch in the y-direction, scale factor 2
- 4Then (x − 3) and − 5 give a translation 3 right and 5 down
- 5Stretch in the y-direction scale factor 2 followed by translation (3, −5)
AnswerStretch in the y-direction, scale factor 2, followed by translation by vector (3, −5)
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