11.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c0b4165d-b8bb-419c-b75a-d6c0c2431510-30_595_869_255_568}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
Figure 5 shows part of the curve \(C\) with equation \(y = \mathrm { f } ( x )\) where
$$f ( x ) = 2 x ^ { 2 } - 12 x + 14$$
- Write \(2 x ^ { 2 } - 12 x + 14\) in the form
$$a ( x + b ) ^ { 2 } + c$$
where \(a\), \(b\) and \(c\) are constants to be found.
Given that \(C\) has a minimum at the point \(P\)
- state the coordinates of \(P\)
The line \(l\) intersects \(C\) at \(( - 1,28 )\) and at \(P\) as shown in Figure 5.
- Find the equation of \(l\) giving your answer in the form \(y = m x + c\) where \(m\) and \(c\) are constants to be found.
The finite region \(R\), shown shaded in Figure 5, is bounded by the \(x\)-axis, \(l\), the \(y\)-axis, and \(C\).
- Use inequalities to define the region \(R\).