Question 3 - A-Level Maths

1. Express $x ^ { 2 } - 4 x + 9$ in the form $( x - p ) ^ { 2 } + q$, where $p$ and $q$ are integers.
2. Hence, or otherwise, state the coordinates of the minimum point of the curve with equation $y = x ^ { 2 } - 4 x + 9$.
The line $L$ has equation $y + 2 x = 12$ and the curve $C$ has equation $y = x ^ { 2 } - 4 x + 9$.
1. Show that the $x$-coordinates of the points of intersection of $L$ and $C$ satisfy the equation $$x ^ { 2 } - 2 x - 3 = 0$$
2. Hence find the coordinates of the points of intersection of $L$ and $C$.