Answer
(a) See graph (red curve).
(b) domain $(-\infty,\infty)$, range $(-\infty,0]$.
(c) increasing on $(-\infty,\frac{5}{2})$, decreasing on $(\frac{5}{2},\infty)$.
Work Step by Step
(a) To graph $y=-4x^2+20x-25=-4(x-\frac{5}{2})^2$, start from $y=x^2$, shift the curve $\frac{5}{2}$ unit(s) to the right, 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 $(-\infty,\frac{5}{2})$, decreasing on $(\frac{5}{2},\infty)$.
