Answer
(a) See graph (red curve).
(b) domain $(-\infty,\infty)$, range $(-\infty,0]$.
(c) increasing on $(-\infty,-\frac{1}{2})$, decreasing on $(-\frac{1}{2},\infty)$.
Work Step by Step
(a) To graph $y=-4x^2-4x-1=-4(x+\frac{1}{2})^2$, start from $y=x^2$, shift the curve $\frac{1}{2}$ unit(s) to the left, stretch vertically be a factor of 4, then reflect across the x-axis. See graph (red curve).
(b) We can determine the domain $(-\infty,\infty)$, range $(-\infty,0]$.
(c) The function is increasing on $(-\infty,-\frac{1}{2})$, decreasing on $(-\frac{1}{2},\infty)$.
