8. \begin{figure}[h] \end{figure} \section*{In this question you must show all stages of your working.} \section*{Solutions relying on calculator technology are not acceptable.} The graph shown in Figure 2 has equation $$y = a - | 2 x - b |$$ where \(a\) and \(b\) are positive constants, \(a > b\)

1. Find, giving your answer in terms of \(a\) and \(b\),
   1. the coordinates of the maximum point of the graph,
   2. the coordinates of the point of intersection of the graph with the \(y\)-axis,
   3. the coordinates of the points of intersection of the graph with the \(x\)-axis. On page 24 there is a copy of Figure 2 called Diagram 1.
2. On Diagram 1, sketch the graph with equation $$y = | x | - 1$$ Given that the graphs \(y = | x | - 1\) and \(y = a - | 2 x - b |\) intersect at \(x = - 3\) and \(x = 5\)
3. find the value of \(a\) and the value of \(b\) \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{76989f19-2624-4e86-a8ee-4978dd1014c2-24_675_652_1959_712} \captionsetup{labelformat=empty} \caption{Diagram 1}
   \end{figure}