Transform a parabola and recover its roots
8 written marks
Let \(f(x)=x^2\), \(x\in\mathbb R\), and \(g(x)=-2f(3x-6)+8\).
Part a · 3 marks
Describe an ordered sequence of stretches, reflections and translations taking the graph of \(f\) to that of \(g\).
Part b · 3 marks
Write \(g(x)\) in completed-square form and state the vertex and range.
Part c · 2 marks
Find the x-intercepts of the graph of \(g\).
Complete-answer checking, worked solutions and indicative written criteria.
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