8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f1e1d4f5-dd27-4839-a6f3-f6906666302c-22_657_659_214_646}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Figure 4 shows a sketch of the curve \(C\) with equation
$$y = 4 + 12 x - 3 x ^ { 2 }$$
The point \(M\) is the maximum turning point on \(C\).
- Write \(4 + 12 x - 3 x ^ { 2 }\) in the form
$$a + b ( x + c ) ^ { 2 }$$
where \(a , b\) and \(c\) are constants to be found.
- Hence, or otherwise, state the coordinates of \(M\).
The line \(l _ { 1 }\) passes through \(O\) and \(M\), as shown in Figure 4.
A line \(l _ { 2 }\) touches \(C\) and is parallel to \(l _ { 1 }\)
- Find an equation for \(l _ { 2 }\)