IB AA HL May 2026 P1 TZA Q1

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]