# How do you find the domain and range for x^2 + 5x + 6?

$f \left(x\right) = {x}^{2} + 5 x + 6 = \left(x + 2\right) \left(x + 3\right)$
$x = - \frac{b}{21} = - \frac{5}{2}$
$y = f \left(- \frac{5}{2}\right) = \frac{25}{4} - \frac{25}{2} + 6 = - \frac{1}{4}$