Answer
(a) See graph, opens up, vertex $(\frac{1}{4},\frac{15}{8})$, axis of symmetry $x=\frac{1}{4}$, y-intercept $(0,2)$,
(b) domain $(-\infty,\infty)$, range $[\frac{15}{8},\infty)$.
(c) increasing on $(\frac{1}{4},\infty)$, decreasing on $(-\infty,\frac{1}{4})$.
Work Step by Step
(a) See graph for $y=2x^2-x+2=2(x-\frac{1}{4})^2+\frac{15}{8}$, we can find that the graph opens up, vertex $(\frac{1}{4},\frac{15}{8})$, axis of symmetry $x=\frac{1}{4}$, y-intercept $(0,2)$, x-intercept(s) $none$.
(b) We can determine the domain $(-\infty,\infty)$, range $[\frac{15}{8},\infty)$.
(c) The function is increasing on $(\frac{1}{4},\infty)$, decreasing on $(-\infty,\frac{1}{4})$.
