(a) Show that \(2x^2+5x+3\) can be written in the form \(2(x+a)^2+b\), where \(a\) and \(b\) are constants to be found.

(b) Hence write down the coordinates of the stationary point on the curve \(y=2x^2+5x+3\).

A function \(\mathrm{f}\) is such that \(\mathrm{f}(x)=2x^2+5x+3\), for \(x\geqslant p\), where \(p\) is a constant. It is given that \(\mathrm{f}^{-1}\) exists.

(c)(i) Write down the least possible value of \(p\).

(ii) Using your value of \(p\), sketch the graphs of \(y=\mathrm{f}(x)\) and \(y=\mathrm{f}^{-1}(x)\). Label each graph. State the intercepts of each of the graphs with the axes.