8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bb21001f-fe68-4776-992d-ede1aae233d7-20_728_885_248_584}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of the straight line \(l\) and the curve \(C\).
Given that \(l\) cuts the \(y\)-axis at - 12 and cuts the \(x\)-axis at 4 , as shown in Figure 2,
- find an equation for \(l\), writing your answer in the form \(y = m x + c\), where \(m\) and \(c\) are constants to be found.
Given that \(C\)
- has equation \(y = \mathrm { f } ( x )\) where \(\mathrm { f } ( x )\) is a quadratic expression
- has a minimum point at \(( 7 , - 18 )\)
- cuts the \(x\)-axis at 4 and at \(k\), where \(k\) is a constant
- deduce the value of \(k\),
- find \(\mathrm { f } ( x )\).
The region \(R\) is shown shaded in Figure 2. - Use inequalities to define \(R\).