(a)[3]
Express $-2x^2 + 8x + 11$ in the form $-a(x - b)^2 + c$, where $a$, $b$ and $c$ are positive integers, and then find the coordinates of the vertex of the graph with equation $y = -2x^2 + 8x + 11$.
(b)[5]
The diagram shows a section of the curve with equation $y = -2x^2 + 8x + 11$ and the line with equation $y = 8x + 9$. Find the area of the shaded region.