By expressing \(- 2 x ^ { 2 } + 8 x + 11\) in the form \(- a ( x - b ) ^ { 2 } + c\), where \(a , b\) and \(c\) are positive integers, find the coordinates of the vertex of the graph with equation \(y = - 2 x ^ { 2 } + 8 x + 11\).
\includegraphics[max width=\textwidth, alt={}, center]{39393c20-34df-4167-a8bf-e4067371de81-10_561_1603_1137_310}
The diagram shows part of the curve with equation \(y = - 2 x ^ { 2 } + 8 x + 11\) and the line with equation \(y = 8 x + 9\).
Find the area of the shaded region.
\includegraphics[max width=\textwidth, alt={}, center]{39393c20-34df-4167-a8bf-e4067371de81-10_2722_43_107_2004}
\includegraphics[max width=\textwidth, alt={}, center]{39393c20-34df-4167-a8bf-e4067371de81-11_2726_35_97_20}