Answer
See graph and explanations.
Work Step by Step
Step 1. Locate the three given points $(-2,8),(0,4),(2,0)$
Step 2. As $f'(2)=f'(-2)=0$, we know these two points will be extrema or inflection points.
Step 3. As $f'(x)\lt0$ when $|x|\lt2$, the function decreases on $(-2,2)$; thus connect a smooth curve between the first and the third points passing the middle point.
Step 4. As $f''(x)\lt0$ when $x\lt0$, the curve is concave down on $x\lt0$; thus point $(-2,8)$ is a maximum.
Step 5. As $f''(x)\gt0$ when $x\gt0$, the curve is concave up on $x\gt0$; thus point $(208)$ is a minimum.
Step 6. As $f'(x)\gt0$ when $|x|\gt2$, the function increases on $(-\infty,-2)$ and $(2,\infty)$; thus draw smooth curves from the first point down to the left and from the third point up to the right.
