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