Functions f and g are both defined for \(x\in\mathbb R\) and are given by \[f(x)=x^2-2x+5,\qquad g(x)=x^2+4x+13.\]

(a) By first expressing each of \(f(x)\) and \(g(x)\) in completed square form, express \(g(x)\) in the form \(f(x+p)+q\), where p and q are constants. [4]

(b) Describe fully the transformation which transforms the graph of \(y=f(x)\) to the graph of \(y=g(x)\). [2]