9709 P12 - Mar 2022 - Q5
649
(a) Express \(2x^2 - 8x + 14\) in the form \(2[(x-a)^2 + b]\).
The functions \(f\) and \(g\) are defined by
\(f(x) = x^2\) for \(x \in \mathbb{R}\),
\(g(x) = 2x^2 - 8x + 14\) for \(x \in \mathbb{R}\).
(b) Describe fully a sequence of transformations that maps the graph of \(y = f(x)\) onto the graph of \(y = g(x)\), making clear the order in which the transformations are applied.
