Answer
Check graph
Work Step by Step
$f(x) = -2(x + 2)(x - 2)^3$
Step 1.
$f(x) = -2x^4 + 8x^3 - 32x + 32$ is a degree 4 polynomial
End behavior as $y = -2x^4$ for large x
Step 2.
Y-Intercept = $f(0) = 32$
X-Intercept when $f(x) = 0$ gives $x = -2, 2$
Step 3.
Zeros of the function are $x = -2, 2$
Multiplicity of Zero -2 is 1(odd) so the graph of f crosses the x-axis at x = -2.
Multiplicity of Zero 2 is 3(odd) so the graph of f crosses the x-axis at x = 2.
Step 4.
Because the polynomial function is of degree 3 (Step 1), the graph of the function will have at most 4 - 1 = 3 turning points.
But since root $x = 2$ is triply repeated, there will be inflection point at $x = 2$ and only single turning point
Step 5.
Finding values of f(x) for some x and plotting the graph using results of step 1 to 4
$f(1) = 6$, $f(-1) = 54$, $f(0) = 32$, $f(3) = -10$