Answer
a) See graph
b) Domain $(-\infty, \infty)$
Range $ [0, \infty)$
c) Decreasing $(-\infty, -3]$
Increasing $[-3, \infty)$
Work Step by Step
$f(x) = x^2 + 6x + 9 = (x+3)^2$
a) $a = 1$, $b = 6$, $c = 9$
a > 0, so graph will open up
vertex $x = \frac{-b}{2a} = -3$
axis of symmetry $x = -3$
Minimum value = $f(-3) = (-3)^2 -18 + 9 = 0$
For x intercept $y = 0$
we get $ x^2 + 6x + 9 = (x+3)^2 = 0$
=> $ x= -3$
y-intercept at $x = 0$, $(0, 9)$
b) Domain $(-\infty, \infty)$
Range$ [0, \infty)$
c) Decreasing $(-\infty, -3]$
Increasing $[-3, \infty)$
