Answer
See graph and explanations.
Work Step by Step
Step 1. Given $f(x)=-2(x-1)^2(x+3)$, we test for symmetry:
$f(-x)=-2(-x-1)^2(-x+3)=2(x+1)^2(x-3)$; no symmetry.
Step 2. End behavior: the leading term $-2x^3$, rises to the left and falls to the right.
Step 3. The x-intercepts are: $x=-3, 1$. The graph crosses the x-axis at $x=-3$, and touches/returns at $x=1$.
Step 4. The y-intercept: $f(0)=-2(1)(3)=-6$
Step 5. The maximum number of turns: $n-1=2$
Step 6. We use the test points as necessary to graph the function as shown in the figure.
