Find the values of the constant \(m\) for which the line \(y = m x\) is a tangent to the curve \(y = 2 x ^ { 2 } - 4 x + 8\).
The function f is defined for \(x \in \mathbb { R }\) by \(\mathrm { f } ( x ) = x ^ { 2 } + a x + b\), where \(a\) and \(b\) are constants. The solutions of the equation \(\mathrm { f } ( x ) = 0\) are \(x = 1\) and \(x = 9\). Find
the values of \(a\) and \(b\),
the coordinates of the vertex of the curve \(y = \mathrm { f } ( x )\).