2 A curve \(C\) has equation \(y = \mathrm { f } ( x )\) where
$$f ( x ) = - 3 x ^ { 2 } + 12 x + 8$$
- Write \(f ( x )\) in the form
$$a ( x + b ) ^ { 2 } + c$$
where \(a\), \(b\) and \(c\) are constants to be found.
The curve \(C\) has a maximum turning point at \(M\).
- Find the coordinates of \(M\).
Solutions relying on calculator technology are not acceptable.
Simplify
$$\frac { \sqrt { } 32 + \sqrt { } 18 } { 3 + \sqrt { } 2 }$$
giving your answer in the form \(b \sqrt { } 2 + c\), where \(b\) and \(c\) are integers.
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