Express \(2 x ^ { 2 } - 8 x + 14\) in the form \(2 \left[ ( x - a ) ^ { 2 } + b \right]\).
The functions \(f\) and \(g\) are defined by
$$\begin{aligned}
& \mathrm { f } ( x ) = x ^ { 2 } \quad \text { for } x \in \mathbb { R }
& \mathrm {~g} ( x ) = 2 x ^ { 2 } - 8 x + 14 \quad \text { for } x \in \mathbb { R }
\end{aligned}$$
Describe fully a sequence of transformations that maps the graph of \(y = \mathrm { f } ( x )\) onto the graph of \(y = \mathrm { g } ( x )\), making clear the order in which the transformations are applied.
\includegraphics[max width=\textwidth, alt={}, center]{05e75fa2-81ae-44b1-b073-4100f5d911e0-08_679_1043_260_552}
The circle with equation \(( x + 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 85\) and the straight line with equation \(y = 3 x - 20\) are shown in the diagram. The line intersects the circle at \(A\) and \(B\), and the centre of the circle is at \(C\).