Answer
a) See graph
b) Domain $(-\infty, \infty)$
Range$ [4.25, -\infty)$
c) Increasing $(-\infty, -0.75]$
Decreasing $[-0.75, \infty)$
Work Step by Step
$f(x) = -4x^2 - 6x + 2$
a) $a = -4$, $b = -6$, $c = 2$
a < 0, so graph will open down
vertex $x = \frac{-b}{2a} = 0.75$
Axis of symmetry $x = -0.75$
Maximum value = $f(-0.75) = -4(-0.75)^2 - 6\times (-0.75) + 2 = 4.25$
For x intercept $y = 0$
we get $-4x^2 - 6x + 2 = 0$
$=> x = \frac{-3 \pm \sqrt{17}}{4}$
y-intercept at $x = 0$, $(0, 2)$
b) Domain $(-\infty, \infty)$
Range$ [4.25, -\infty)$
c) Increasing $(-\infty, -0.75]$
Decreasing $[-0.75, \infty)$
