Express \(2 x ^ { 2 } + 8 x - 10\) in the form \(a ( x + b ) ^ { 2 } + c\).
For the curve \(y = 2 x ^ { 2 } + 8 x - 10\), state the least value of \(y\) and the corresponding value of \(x\).
Find the set of values of \(x\) for which \(y \geqslant 14\).
Given that \(\mathrm { f } : x \mapsto 2 x ^ { 2 } + 8 x - 10\) for the domain \(x \geqslant k\),
find the least value of \(k\) for which f is one-one,
express \(\mathrm { f } ^ { - 1 } ( x )\) in terms of \(x\) in this case.