Answer
(a) See graph
(b) domain $(-\infty,\infty)$, range $[-\frac{7}{3},\infty)$.
(c) decreasing on $(-\infty,-\frac{2}{3})$, increasing on $(-\frac{2}{3},\infty)$.
Work Step by Step
(a) For $y=3x^2+4x-1=3(x^2+\frac{4}{3}x+(\frac{2}{3})^2)-\frac{7}{3}=3(x+\frac{2}{3})^2-\frac{7}{3}$, we can determining that the graph opens up, vertex $(-\frac{2}{3},-\frac{7}{3})$, axis of symmetry $x=-\frac{2}{3}$, y-intercept $(0,-1)$, x-intercept(s) $(-1.55,0),(0.22,0)$. See graph
(b) We can determine the domain $(-\infty,\infty)$, range $[-\frac{7}{3},\infty)$.
(c) We can determine the function is decreasing on $(-\infty,-\frac{2}{3})$, increasing on $(-\frac{2}{3},\infty)$.
