2019 A-Level H2 Mathematics

A function is defined as \(\mathrm{f}\left( x \right)=2{{x}^{3}}-6{{x}^{2}}+6x-12\).

1. Show that \(\mathrm{f}\left( x \right)\) can be written in the form \(p\left\{ {{\left( x+q \right)}^{3}}+r \right\}\), where \(p,q\) and \(r\) are constants to be found.[2]
2. Hence, or otherwise, describe a sequence of transformations that transform the graph of \(y={{x}^{3}}\) onto the graph of \(y=\mathrm{f}\left( x \right)\).[3]