Answer
(a) See graph, opens up, vertex $(\frac{4}{3},-\frac{10}{3})$, axis of symmetry $x=\frac{4}{3}$, y-intercept $(0,2)$, x-intercept(s) $(2.39,0),(0.28,0)$.
(b) domain $(-\infty,\infty)$, range $[-\frac{10}{3},\infty)$.
(c) increasing on $(\frac{4}{3},\infty)$, decreasing on $(-\infty,\frac{4}{3})$.
Work Step by Step
(a) See graph for $y=3x^2-8x+2=3(x-\frac{4}{3})^2-\frac{10}{3}$, we can find that the graph opens up, vertex $(\frac{4}{3},-\frac{10}{3})$, axis of symmetry $x=\frac{4}{3}$, y-intercept $(0,2)$, x-intercept(s) $(2.39,0),(0.28,0)$.
(b) We can determine the domain $(-\infty,\infty)$, range $[-\frac{10}{3},\infty)$.
(c) The function is increasing on $(\frac{4}{3},\infty)$, decreasing on $(-\infty,\frac{4}{3})$.
