Answer
See graph.
Work Step by Step
Step 1. Given $f(x)=x^4-3x^2+2=(x^2-1)(x^2-2)=(x+1)(x-1)(x+\sqrt 2)(x-\sqrt 2)$, we can find its zeros as $x=\pm1,\pm\sqrt 2$, y-intercept $f(0)=2$. Function is even. End behavior: rise to the right and rise to the left. Maximum number of turning points $3$.
Step 2. Use the information above and test point to graph the function as shown in the figure.