10 A curve has equation \(y = 2 x ^ { 2 } - 3 x\).
- Find the set of values of \(x\) for which \(y > 9\).
- Express \(2 x ^ { 2 } - 3 x\) in the form \(a ( x + b ) ^ { 2 } + c\), where \(a , b\) and \(c\) are constants, and state the coordinates of the vertex of the curve.
The functions f and g are defined for all real values of \(x\) by
$$\mathrm { f } ( x ) = 2 x ^ { 2 } - 3 x \quad \text { and } \quad \mathrm { g } ( x ) = 3 x + k$$
where \(k\) is a constant.
- Find the value of \(k\) for which the equation \(\mathrm { gf } ( x ) = 0\) has equal roots.