The line $x - y + 4 = 0$ meets the curve $y = 2x^2 - 4x + 1$ at the points $P$ and $Q$. The coordinates of $P$ are given as $(3, 7)$.
(i)[4]
Rewrite $2x^2 - 4x + 1$ in the form $a(x + b)^2 + c$ and hence give the coordinates of the minimum point, $A$, on the curve $y = 2x^2 - 4x + 1$.
(ii)[3]
Determine the coordinates of $Q$.
(iii)[3]
Determine the equation of the line that passes through $Q$ and the midpoint of $AP$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Shows the quadratic as $2(x-1)^2-1$ or determines $a=2,b=-1,c=-1$” …