Answer
See graph, axis of symmetry $x=1$
domain $(-\infty,\infty)$, range $(- \infty,4]$
Work Step by Step
Step 1. Given $f(x)=-x^2+2x+3=-(x^2-2x+1)+4=-(x-1)^2+4$, we can identify its vertex at $(1,4)$
Step 2. The x-intercept can be found by letting $y=0$, which gives $(x-1)^2=4$ and $x=-1,3$
Step 3. The y-intercept can be found by letting $x=0$, which gives $y=3$
Step 4. Sketch the function as shown in the figure.
Step 5. The axis of symmetry can be identified as $x=1$
Step 6. The domain can be found to be $(-\infty,\infty)$ and the range to be $(- \infty,4]$
