Answer
See graph, axis of symmetry $x=-4$,
domain $(-\infty,\infty)$, range $[-2, \infty)$
Work Step by Step
Step 1. Given $f(x)=(x+4)^2-2$, we can identify its vertex at $(-4,-2)$
Step 2. The x-intercept can be found by letting $y=0$, which gives $(x+4)^2=2$ and $x=-4\pm\sqrt 2$
Step 3. The y-intercept can be found by letting $x=0$, which gives $y=14$
Step 4. Sketch the function as shown in the figure.
Step 5. The axis of symmetry can be identified as $x=-4$
Step 6. The domain can be found to be $(-\infty,\infty)$ and the range to be $[-2, \infty)$
