2026 MAY TZA P1 Q2

Consider the function \(f(x) = 3(x - 2)(x - q)\), where \(x \in \mathbb{R}\) and \(q\) is a real constant.
The axis of symmetry of the graph of \(f\) has equation \(x = 4\).

1. Show that \(q = 6\).

   [2]

2. Find the coordinates of the vertex of the graph of \(f\).

   [2]

3. Hence, write down the range of \(f\).

   [1]