Unknown root of a quadratic in factorised form from its axis of symmetry, then its vertex 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 graph of \(y=g(x)\) is symmetrical about the line \(x=2\).

1. Show that \(p=5\).[2]
2. Find the maximum point of the graph of \(y=g(x)\), giving its coordinates.[2]
3. Hence write down the set of values that \(g(x)\) can take.[1]