9 The equation of a curve is given by \(y = ( x - 1 ) ^ { 2 } ( x + 2 )\).
- Write \(( x - 1 ) ^ { 2 } ( x + 2 )\) in the form \(x ^ { 3 } + p x ^ { 2 } + q x + r\) where \(p , q\) and \(r\) are to be determined.
- Show that the curve \(y = ( x - 1 ) ^ { 2 } ( x + 2 )\) has a maximum point when \(x = - 1\) and find the coordinates of the minimum point.
- Sketch the curve \(y = ( x - 1 ) ^ { 2 } ( x + 2 )\).
- For what values of \(k\) does \(( x - 1 ) ^ { 2 } ( x + 2 ) = k\) have exactly one root.