2008 AJC P1 Q9

A sketch of the curve \(\mathrm{f}(x)=\frac{a{{x}^{2}}+bx}{2{{x}^{2}}-k}\), where \(a\), \(b\) and \(k\) are non-zero constants, is shown above.

Explain why \(a=4\) and \(k<0\). Using the given graph,

1. Sketch the graph of \(\mathrm{f}(x)=\frac{a{{x}^{2}}-bx}{2{{x}^{2}}-k}\)for all values of \(x\).
2. Determine the number of stationary points of the curve whose equation is \(y={{[\mathrm{f}(x)]}^{2}}\).