Answer
a) See graph
b) Domain $(-\infty, \infty)$
Range$ [1.875, \infty)$
c) Decreasing $(-\infty, 0.25]$
Increasing $[0.25, \infty)$
Work Step by Step
$f(x) = 2x^2 - x + 2 = (x+3)^2$
a) $a = 2$, $b = -1$, $c = 2$
a > 0, so graph will open up
vertex $x = \frac{-b}{2a} = 0.25$
axis of symmetry $x = 0.25$
Minimum value = $f(0.25) = 2(0.25)^2 -0.25 + 2 = 1.875$
For x intercept $y = 0$
we get $ 2x^2 - x + 2 = 0$
=>Discriminant of quadratic is negative so no intercepts
y-intercept at $x = 0$, $(0, 2)$
b) Domain $(-\infty, \infty)$
Range$ [1.875, \infty)$
c) Decreasing $(-\infty, 0.25]$
Increasing $[0.25, \infty)$
