Answer
a) See graph
b) Domain $(-\infty, \infty)$
Range$ [-1.25, -\infty)$
c) Increasing $(-\infty, 0.5]$
Decreasing $[0.5, \infty)$
Work Step by Step
$f(x) = -3x^2 + 3x - 2$
a) $a = -3$, $b = 3$, $c = -2$
a < 0, so graph will open down
vertex $x = \frac{-b}{2a} = 0.5$
Axis of symmetry $x = 0.5$
Maximum value = $f(0.5) = -3(0.5)^2 +3 \times 0.5 -2 = -1.25$
For x intercept $y = 0$
we get $-3x^2 + 3x - 2 = 0$
=>Discriminant of quadratic is negative(-15) so no x-intercepts
y-intercept at $x = 0$, $(0, -2)$
b) Domain $(-\infty, \infty)$
Range$ [-1.25, -\infty)$
c) Increasing $(-\infty, 0.5]$
Decreasing $[0.5, \infty)$