Answer
(a) See graph (red curve).
(b) domain $(-\infty,\infty)$, range $[\frac{7}{8},\infty)$.
(c) decreasing on $(-\infty,-\frac{1}{4})$, increasing on $(-\frac{1}{4},\infty)$.
Work Step by Step
(a) To graph $y=2x^2+x+1=2(x+\frac{1}{4})^2+\frac{7}{8}$, start from $y=x^2$, shift the curve $\frac{1}{4}$ unit(s) to the left, stretch vertically by a factor of 2, then shift $\frac{7}{8}$ unit(s) up. See graph (red curve).
(b) We can determine the domain $(-\infty,\infty)$, range $[\frac{7}{8},\infty)$.
(c) The function is decreasing on $(-\infty,-\frac{1}{4})$, increasing on $(-\frac{1}{4},\infty)$.
