(a)[2]
Write $-3x^2 + 12x + 2$ in the form $-3(x - a)^2 + b$, where $a$ and $b$ are constants.
(b)[1]
State the greatest possible value of the constant $k$.
(c)[1]
Now that $k = -1$ is given, state the range of $f$.
(d)[3]
Find an expression for $f^{-1}(x)$.
(e)[3]
After the graph of $y = f(x)$ is translated by $\begin{pmatrix}-3\\1\end{pmatrix}$, it becomes the graph of $y = g(x)$. Write $g(x)$ in the form $px^2 + qx + r$, where $p$, $q$ and $r$ are constants.