8 The function f is defined by \(\mathrm { f } ( x ) = a + b \cos 2 x\), for \(0 \leqslant x \leqslant \pi\). It is given that \(\mathrm { f } ( 0 ) = - 1\) and \(\mathrm { f } \left( \frac { 1 } { 2 } \pi \right) = 7\).
- Find the values of \(a\) and \(b\).
- Find the \(x\)-coordinates of the points where the curve \(y = \mathrm { f } ( x )\) intersects the \(x\)-axis.
- Sketch the graph of \(y = \mathrm { f } ( x )\).