(a)[3]
Determine the values of the constant $m$ for which the line $y = mx$ is tangent to the curve $y = 2x^2 - 4x + 8$.
(b(i))[2]
The function $f$ is defined for $x \in \mathbb{R}$ by $f(x) = x^2 + ax + b$, where $a$ and $b$ are constants. The roots of the equation $f(x) = 0$ are $x = 1$ and $x = 9$. Determine the values of $a$ and $b$.
(b(ii))[2]
Determine the coordinates of the vertex of the curve $y = f(x)$.