(a)[2]
Find the coordinates of the curve's minimum point.
(b)[2]
The curve is stretched by a factor of $2$ parallel to the $y$-axis and then translated by $\begin{pmatrix}4 \\ 1\end{pmatrix}$. Find the coordinates of the minimum point of the transformed curve.
(c)[4]
Find the equation of the transformed curve. Give the answer in the form $y = ax^2 + bx + c$, with $a$, $b$ and $c$ as integers to be found.