10. The curve \(C _ { 1 }\) has equation \(y = \mathrm { f } ( x )\), where
$$f ( x ) = ( 4 x - 3 ) ( x - 5 ) ^ { 2 }$$
- Sketch \(C _ { 1 }\) showing the coordinates of any point where the curve touches or crosses the coordinate axes.
- Hence or otherwise
- find the values of \(x\) for which \(\mathrm { f } \left( \frac { 1 } { 4 } x \right) = 0\)
- find the value of the constant \(p\) such that the curve with equation \(y = \mathrm { f } ( x ) + p\) passes through the origin.
A second curve \(C _ { 2 }\) has equation \(y = \mathrm { g } ( x )\), where \(\mathrm { g } ( x ) = \mathrm { f } ( x + 1 )\)
- Find, in simplest form, \(\mathrm { g } ( x )\). You may leave your answer in a factorised form.
- Hence, or otherwise, find the \(y\) intercept of curve \(C _ { 2 }\)