Answer
a) See graph
b) Domain $(-\infty, \infty)$
Range$ [-2.5, -\infty)$
c) Decreasing $(-\infty, 0.5]$
Increasing $[0.5, \infty)$
Work Step by Step
$f(x) = -2x^2 + 2x - 3$
a) $a = -2$, $b = 2$, $c = -3$
a < 0, so graph will open down
vertex $x = \frac{-b}{2a} = 0.5$
axis of symmetry $x = 0.5$
Minimum value = $f(0.5) = -2(0.5)^2 +2 \times 0.5 -3 = -2.5$
For x intercept $y = 0$
we get $ -2x^2 + 2x - 3 = 0$
=>Discriminant of quadratic is negative(-20) so no x-intercepts
y-intercept at $x = 0$, $(0, -3)$
b) Domain $(-\infty, \infty)$
Range$ [-2.5, -\infty)$
c) Decreasing $(-\infty, 0.5]$
Increasing $[0.5, \infty)$
