Quadratic in factorised form from its axis of symmetry, with turning point and range

The function \(g\) is defined by \(g(x)=2(x+1)(x-p)\) for \(x\in\mathbb{R}\), where \(p\) is a constant. The minimum point of the graph of \(y=g(x)\) lies on the line \(x=3\).

1. Show that \(p=7\).[2]
2. Find the coordinates of the minimum point of the graph of \(y=g(x)\).[2]
3. Hence, state the range of \(g\).[1]