- The curve \(C\) has equation \(y = \mathrm { f } ( x )\)
Given that
- \(\mathrm { f } ( x )\) is a quadratic expression
- the maximum turning point on \(C\) has coordinates \(( - 2,12 )\)
- \(C\) cuts the negative \(x\)-axis at - 5
- find \(\mathrm { f } ( x )\)
The line \(l _ { 1 }\) has equation \(y = \frac { 4 } { 5 } x\)
Given that the line \(l _ { 2 }\) is perpendicular to \(l _ { 1 }\) and passes through \(( - 5,0 )\)
find an equation for \(l _ { 2 }\), writing your answer in the form \(y = m x + c\) where \(m\) and \(c\) are constants to be found.
(3)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3cf69966-e825-4ff0-a6e8-c5dfdc92c53f-10_983_712_1126_616}
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\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of the curve \(C\) and the lines \(l _ { 1 }\) and \(l _ { 2 }\)Define the region \(R\), shown shaded in Figure 2, using inequalities.