The curve \(C\) has equation
$$y = \frac { a x ^ { 2 } + b x + c } { x + d }$$
where \(a , b , c\) and \(d\) are constants. The curve cuts the \(y\)-axis at \(( 0 , - 2 )\) and has asymptotes \(x = 2\) and \(y = x + 1\).
- Write down the value of \(d\).
- Determine the values of \(a , b\) and \(c\).
- Show that, at all points on \(C\), either \(y \leqslant 3 - 2 \sqrt { 6 }\) or \(y \geqslant 3 + 2 \sqrt { 6 }\).