11. Given that
$$f ( x ) = 2 x ^ { 2 } + 8 x + 3$$
- find the value of the discriminant of \(\mathrm { f } ( x )\).
- Express \(\mathrm { f } ( x )\) in the form \(p ( x + q ) ^ { 2 } + r\) where \(p , q\) and \(r\) are integers to be found.
The line \(y = 4 x + c\), where \(c\) is a constant, is a tangent to the curve with equation \(y = \mathrm { f } ( x )\).
- Calculate the value of \(c\).