Answer
(a) See graph.
(b) $(-\infty,\infty)$.
Work Step by Step
(a) Given $f(x)=-x^2+2x-3=-(x^2-2x+1)-2=-(x-1)^2-2$, we can find its graph opens down, vertex $(1,-2)$, axis of symmetry $x=1$, intercept(s) $(0,-3)$. See graph.
(b) For $f(x)\le0$, we can find the solution $(-\infty,\infty)$.
