8.
$$f ( x ) = 9 + 6 x - x ^ { 2 } .$$
- Find the values of \(A\) and \(B\) such that
$$\mathrm { f } ( x ) = A - ( x + B ) ^ { 2 }$$
- State the maximum value of \(\mathrm { f } ( x )\).
- Solve the equation \(\mathrm { f } ( x ) = 0\), giving your answers in the form \(a + b \sqrt { 2 }\) where \(a\) and \(b\) are integers.
- Sketch the curve \(y = \mathrm { f } ( x )\).