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The quadratic function \(f(x)\), for \(0 \leq x \leq 4\), is shown below.

The curve passes through the point \(P(0; 13)\), and its vertex is the point \(V(2; 1)\).

1. The function can be written in the form \(f(x) = a(x-h)^2 + k\).
   1. Find the value of \(h\) and the value of \(k\).
   2. Show that \(a=3\).
2. Calculate the area bounded by the curve of \(f\), the \(x\)-axis, and the lines \(x=2\) and \(x=4\).