The curve \(C\) has equation
$$y = \frac { a x ^ { 2 } + b x + c } { x + 4 }$$
where \(a\), \(b\) and \(c\) are constants. It is given that \(y = 2 x - 5\) is an asymptote of \(C\).
- Find the values of \(a\) and \(b\).
- Given also that \(C\) has a turning point at \(x = - 1\), find the value of \(c\).
- Find the set of values of \(y\) for which there are no points on \(C\).
- Draw a sketch of the curve with equation
$$y = \frac { 2 ( x - 7 ) ^ { 2 } + 3 ( x - 7 ) - 2 } { x - 3 }$$
[You should state the equations of the asymptotes and the coordinates of the turning points.]