a) \[y = f\left( x \right) = \frac{{{x^2} + 2\left( {m - 1} \right)x + {m^2} + 3m + 5}}\]., a) \(y = f\left( x \right) = \frac{{{x^2} + 2\left( {m - 1} \right)x + {m^2} + 3m + 5}}\).