Answer
See graph.
Work Step by Step
Step 1. Given $f(x)=-2x^3+7x^2-2x-3=-(x-1)(x-3)(2x+1)$, we can find its zeros as $x=1,3,-1/2$, y-intercept $f(0)=-3$. Function is neither even nor odd. End behavior: rise to the left and fall to the right. Maximum of turning points $2$.
Step 2. Use the information above and test point to graph the function as shown in the figure.