Answer
see graph; axis of symmetry $x=-1$,
domain $(-\infty,\infty)$, range $(-\infty,4]$
Work Step by Step
Step 1. Given $f(x)=-(x+1)^2+4$, 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 $x=-3, 1$
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 $(-\infty,4]$
