6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a9870c94-0910-46ec-a54a-44a431cb324e-14_988_1120_123_395}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of the graph with equation \(y = | 4 x + 10 a |\), where \(a\) is a positive constant.
The graph cuts the \(y\)-axis at the point \(P\) and meets the \(x\)-axis at the point \(Q\) as shown.
- State the coordinates of \(P\).
- State the coordinates of \(Q\).
- A copy of Figure 1 is shown on page 15. On this copy, sketch the graph with equation
$$y = | x | - a$$
Show on the sketch the coordinates of each point where your graph cuts or meets the coordinate axes.
- Hence, or otherwise, solve the equation
$$| 4 x + 10 a | = | x | - a$$
giving your answers in terms of \(a\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a9870c94-0910-46ec-a54a-44a431cb324e-15_860_1128_447_392}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
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