3. The function f is even and has domain \(\mathbb { R }\). For \(x \geq 0 , \mathrm { f } ( x ) = x ^ { 2 } - 4 a x\), where \(a\) is a positive constant.
- In the space below, sketch the curve with equation \(y = \mathrm { f } ( x )\), showing the coordinates of all the points at which the curve meets the axes.
- Find, in terms of \(a\), the value of \(\mathrm { f } ( 2 a )\) and the value of \(\mathrm { f } ( - 2 a )\).
Given that \(a = 3\),
- use algebra to find the values of \(x\) for which \(\mathrm { f } ( x ) = 45\).