4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{624e9e2f-b6b8-47ce-accc-31dcd5f0554e-10_646_762_264_593}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of the graph with equation \(y = \mathrm { f } ( x )\), where
$$\mathrm { f } ( x ) = | 3 x + a | + a$$
and where \(a\) is a positive constant.
The graph has a vertex at the point \(P\), as shown in Figure 2 .
- Find, in terms of \(a\), the coordinates of \(P\).
- Sketch the graph with equation \(y = g ( x )\), where
$$g ( x ) = | x + 5 a |$$
On your sketch, show the coordinates, in terms of \(a\), of each point where the graph cuts or meets the coordinate axes.
The graph with equation \(y = \mathrm { g } ( x )\) intersects the graph with equation \(y = \mathrm { f } ( x )\) at two points.
- Find, in terms of \(a\), the coordinates of the two points.
\includegraphics[max width=\textwidth, alt={}, center]{624e9e2f-b6b8-47ce-accc-31dcd5f0554e-11_2255_50_314_34}
| VIXV SIHIANI III IM IONOO | VIAV SIHI NI JYHAM ION OO | VI4V SIHI NI JLIYM ION OO |