Answer
(a) See graph, opens down, vertex $(\frac{1}{2},-\frac{5}{2})$, axis of symmetry $x=\frac{1}{2}$, y-intercept $(0,-3)$,
(b) domain $(-\infty,\infty)$, range $(-\infty,-\frac{5}{2}]$.
(c) decreasing on $(\frac{1}{2},\infty)$, increasing on $(-\infty,\frac{1}{2})$.
Work Step by Step
(a) See graph for $y=-2x^2+2x-3=-2(x-\frac{1}{2})^2-\frac{5}{2}$, we can find that the graph opens down, vertex $(\frac{1}{2},-\frac{5}{2})$, axis of symmetry $x=\frac{1}{2}$, y-intercept $(0,-3)$, x-intercept(s) $none$.
(b) We can determine the domain $(-\infty,\infty)$, range $(-\infty,-\frac{5}{2}]$.
(c) The function is decreasing on $(\frac{1}{2},\infty)$, increasing on $(-\infty,\frac{1}{2})$.
