2025 WGS P2 Q9

The diagram shows part of the curve \(y=x^2+1\), the line \(y=2x+4\).

The curve and the line intersect at the points \(P\) and \(Q\).

Region \(S\) is bounded by the curve \(y=x^2+1\), the line \(y=2x+4\), the \(x\)-axis and the \(y\)-axis.

1. Find the coordinates of \(P\) and \(Q\).[3]
2. Find the area of the shaded region \(S\).[6]