Write \(3 x ^ { 2 } + 24 x + 5\) in the form \(a ( x + b ) ^ { 2 } + c\), where \(a , b\) and \(c\) are constants to be determined.
The finite region \(R\) is enclosed by the curve \(y = 3 x ^ { 2 } + 24 x + 5\) and the \(x\)-axis.
State the inequalities that define \(R\), including its boundaries.