Differentiation - Tangents and Normals at a Point

The function \(f\) is defined by \(f(x) = -0.5x^2 + 2x +2.5\).

Let \(N\) be the normal to the curve at the point where the graph intercepts the \(y\)-axis.

1. Show that the equation of \(N\) may be written as \(y = -0.5x + 2.5\).[4]
2. Find the coordinates of the other point of intersection of the normal and the curve.[5]
3. Let \(R\) be the region enclosed between the curve and \(N\). Find the area of \(R\).[4]