2025 NOV TZ1 P1 Q4

A line with the equation \(y = -3x + 9\) intersects the axes at the points \(\mathrm{P} \ (0, 9)\) and \(\mathrm{Q} \ (3,0)\)
A parabola of the form \(y = ax^2 + c\), where \(a, c \in \mathbb{Z}\), also passes through the points \(\mathrm{P}\) and \(\mathrm{Q}\).
This is shown in the following diagram.

1. [3]

   1. Write down the value of \(c|).

   2. Find the value of \(a\).

The region enclosed by the line and the parabola is shaded in the following diagram.

2. Find the area of the shaded region.

   [4]