6.
$$f ( x ) = 2 x ^ { 2 } - 4 x + 1$$
- Find the values of the constants \(a\), \(b\) and \(c\) such that
$$\mathrm { f } ( x ) = a ( x + b ) ^ { 2 } + c .$$
- State the equation of the line of symmetry of the curve \(y = \mathrm { f } ( x )\).
- Solve the equation \(\mathrm { f } ( x ) = 3\), giving your answers in exact form.