(a) Express \(2x^2-8x+14\) in the form \(2[(x-a)^2+b]\). [2]

The functions \(f\) and \(g\) are defined by \[f(x)=x^2\quad(x\in\mathbb R),\qquad g(x)=2x^2-8x+14\quad(x\in\mathbb R).\]

(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. [4]