- The curve \(C _ { 1 }\) has equation \(y = \mathrm { f } ( x )\).
Given that
- \(\mathrm { f } ( x )\) is a quadratic expression
- \(C _ { 1 }\) has a maximum turning point at \(( 2,20 )\)
- \(C _ { 1 }\) passes through the origin
- sketch a graph of \(C _ { 1 }\) showing the coordinates of any points where \(C _ { 1 }\) cuts the coordinate axes,
- find an expression for \(\mathrm { f } ( x )\).
The curve \(C _ { 2 }\) has equation \(y = x \left( x ^ { 2 } - 4 \right)\)
Curve \(C _ { 1 }\) and \(C _ { 2 }\) meet at the origin, and at the points \(P\) and \(Q\)
Given that the \(x\) coordinate of the point \(P\) is negative,
using algebra and showing all stages of your working, find the coordinates of \(P\)