Answer
a) See graph
b) Domain $(-\infty, \infty)$
Range$ [-0.125, \infty)$
c) Decreasing $(-\infty, -1.25]$
Increasing $[-1.25, \infty)$
Work Step by Step
$f(x) = 2x^2 + 5x + 3 $
a) $a = 2$, $b = 5$, $c = 3$
a > 0, so graph will open upwards
vertex $x = \frac{-b}{2a} = -1.25$
Axis of symmetry $x = 1.25$
Minimum value = $f(1.25) = 2(-1.25)^2 + 5\times (-1.25) + 3 = -0.125$
For x intercept $y = 0$
we get $2x^2 + 5x + 3 = 0$
$=> x = -1, -1.5$
y-intercept at $x = 0$, $(0, 3)$
b) Domain $(-\infty, \infty)$
Range$ [-0.125, \infty)$
c) Decreasing $(-\infty, -1.25]$
Increasing $[-1.25, \infty)$
