9 Functions f and g are both defined for \(x \in \mathbb { R }\) and are given by
$$\begin{aligned}
& \mathrm { f } ( x ) = x ^ { 2 } - 4 x + 9
& \mathrm {~g} ( x ) = 2 x ^ { 2 } + 4 x + 12
\end{aligned}$$
- Express \(\mathrm { f } ( x )\) in the form \(( x - a ) ^ { 2 } + b\).
- Express \(\mathrm { g } ( x )\) in the form \(2 \left[ ( x + c ) ^ { 2 } + d \right]\).
- Express \(\mathrm { g } ( x )\) in the form \(k \mathrm { f } ( x + h )\), where \(k\) and \(h\) are integers.
- Describe fully the two transformations that have been combined to transform the graph of \(y = \mathrm { f } ( x )\) to the graph of \(y = \mathrm { g } ( x )\).