2 A function f is defined by \(\mathrm { f } ( x ) = x ^ { 2 } - 2 x + 5\) for \(x \in \mathbb { R }\). A sequence of transformations is applied in the following order to the graph of \(y = \mathrm { f } ( x )\) to give the graph of \(y = \mathrm { g } ( x )\). Stretch parallel to the \(x\)-axis with scale factor \(\frac { 1 } { 2 }\)
Reflection in the \(y\)-axis
Stretch parallel to the \(y\)-axis with scale factor 3
Find \(\mathrm { g } ( x )\), giving your answer in the form \(a x ^ { 2 } + b x + c\), where \(a , b\) and \(c\) are constants.