Problem

(a) By expressing $-2x^2+8x+11$ 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 $y=-2x^2+8x+11$.

(b)

The diagram shows part 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.