a) Express $2{x^2} - 4x + 1$ in the form $\alpha {\left( {x + b} \right)^2} + c$ and hence state the coordinates of the minimum point, $A$, on the curve $y = 2{x^2} - 4x + 1$.
The line $x - y + 4 = 0$ intersects the curve $y = 2{x^2} - 4x + 1$ at points $P$ and $Q$. It is given that the coordinates of $P$ are $\left( {3,{\text{ }}7} \right)$.
b) Find the coordinates of $Q$.
c) Find the equation of the line joining $Q$ to the mid-point of $AP$.
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