4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6c320b71-8793-461a-a078-e4f64c144a3a-10_689_917_264_507}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
\section*{In this question you must show all stages of your working.}
\section*{Solutions relying on calculator technology are not acceptable.}
Figure 1 shows a line \(l\) with equation \(x + y = 6\) and a curve \(C\) with equation \(y = 6 x - 2 x ^ { 2 } + 1\)
The line \(l\) intersects the curve \(C\) at the points \(P\) and \(Q\) as shown in Figure 1.
- Find, using algebra, the coordinates of \(P\) and the coordinates of \(Q\).
The region \(R\), shown shaded in Figure 1, is bounded by \(C , l\) and the \(x\)-axis.
- Use inequalities to define the region \(R\).
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