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