2.4: Completed square and inverse sketch

Express $f(x)$ in the form $a(x - b)^{2} + c$, where $a$, $b$ and $c$ are constants.

On the same axes, sketch the graphs of $y = f(x)$ and $y = f^{-1}(x)$, showing the geometrical relationship between them.

Using your answer from part (i), find an expression for $f^{-1}(x)$, stating its domain.