(a)[2]
Rewrite $2x^2 - 8x + 14$ in the form $2[(x - a)^2 + b]$.
(b)[4]
The functions $f$ and $g$ are given by $f(x) = x^2$ for $x \in \mathbb{R}$ and $g(x) = 2x^2 - 8x + 14$ for $x \in \mathbb{R}$. Describe fully a sequence of transformations that carries the graph of $y = f(x)$ onto the graph of $y = g(x)$, and state clearly the order in which those transformations occur.