9.
\includegraphics[max width=\textwidth, alt={}, center]{61af807c-1f2c-417a-85cf-86f2cf566cb9-3_670_1022_1263_374}
The diagram shows the curve \(y = 2 x ^ { 2 } + 6 x + 7\) and the straight line \(y = 2 x + 13\).
- Find the coordinates of the points where the curve and line intersect.
- Show that the area of the shaded region bounded by the curve and line is given by
$$\int _ { - 3 } ^ { 1 } \left( 6 - 4 x - 2 x ^ { 2 } \right) d x$$
- Hence find the area of the shaded region.