3. In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{50ec901b-b6b6-4b72-85bd-a084f313c99b-06_583_588_395_680}
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\caption{Figure 2}
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Figure 2 shows a sketch of the curve \(C\) with equation \(y = x ^ { 2 } - 5 x + 13\)
The point \(M\) is the minimum point of \(C\).
The straight line \(l\) passes through the origin \(O\) and intersects \(C\) at the points \(M\) and \(N\) as shown.
Find, showing your working,
- the coordinates of \(M\),
- the coordinates of \(N\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{50ec901b-b6b6-4b72-85bd-a084f313c99b-06_531_561_1793_680}
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\caption{Figure 3}
\end{figure}
Figure 3 shows the curve \(C\) and the line \(l\). The finite region \(R\), shown shaded in Figure 3, is bounded by \(C , l\) and the \(y\)-axis. - Use inequalities to define the region \(R\).