A curve has equation \(y = 8 - 4 x - 2 x ^ { 2 }\).
Find the values of \(x\) where the curve crosses the \(x\)-axis, giving your answer in the form \(m \pm \sqrt { n }\), where \(m\) and \(n\) are integers.
Sketch the curve, giving the value of the \(y\)-intercept.
A line has equation \(y = k ( x + 4 )\), where \(k\) is a constant.
Show that the \(x\)-coordinates of any points of intersection of the line with the curve \(y = 8 - 4 x - 2 x ^ { 2 }\) satisfy the equation
$$2 x ^ { 2 } + ( k + 4 ) x + 4 ( k - 2 ) = 0$$
Find the values of \(k\) for which the line is a tangent to the curve \(y = 8 - 4 x - 2 x ^ { 2 }\). [0pt]
[3 marks]