9.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{cfc23548-bf4f-4efa-9ceb-b8d03bb1f019-13_698_1413_118_280}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of the curve \(C\) with equation \(y = \mathrm { f } ( x )\).
The curve \(C\) passes through the point \(( - 1,0 )\) and touches the \(x\)-axis at the point \(( 2,0 )\).
The curve \(C\) has a maximum at the point ( 0,4 ).
- The equation of the curve \(C\) can be written in the form
$$y = x ^ { 3 } + a x ^ { 2 } + b x + c$$
where \(a\), \(b\) and \(c\) are integers.
Calculate the values of \(a , b\) and \(c\). - Sketch the curve with equation \(y = \mathrm { f } \left( \frac { 1 } { 2 } x \right)\) in the space provided on page 24
Show clearly the coordinates of all the points where the curve crosses or meets the coordinate axes.