Answer
See graph.
Work Step by Step
Step 1. Given $f(x)=-2x^4+7x^3-4x^2-4x=x(2x+1)(x-2)^2$, we can find its zeros as $x=-1/2,0$ and $x=2$ (multiplicity 2), y-intercept $f(0)=0$. Function is neither even nor odd. End behavior: fall to the right and fall to the left. Maximum number of turning points $3$.
Step 2. Use the information above and test points to graph the function as shown in the figure.