- A curve \(C\) has equation \(y = \mathrm { f } ( x )\) where
$$f ( x ) = - 3 x ^ { 2 } + 12 x + 8$$
- Write \(\mathrm { f } ( x )\) in the form
$$a ( x + b ) ^ { 2 } + c$$
where \(a\), \(b\) and \(c\) are constants to be found.
The curve \(C\) has a maximum turning point at \(M\).
- Find the coordinates of \(M\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{235cd1dc-a3ab-473a-bf77-3e41b274dfd8-34_735_841_913_612}
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\caption{Figure 3}
\end{figure}
Figure 3 shows a sketch of the curve \(C\).
The line \(l\) passes through \(M\) and is parallel to the \(x\)-axis.
The region \(R\), shown shaded in Figure 3, is bounded by \(C , l\) and the \(y\)-axis. - Using algebraic integration, find the area of \(R\).