#### Answer

-8

#### Work Step by Step

We are given that $f(x)=-2x^{2}+3x-6$. In order to evaluate at $f(-\frac{1}{2})$, we can plug $-\frac{1}{2}$ into the function and evaluate.
$f(-\frac{1}{2})=-2(-\frac{1}{2})^{2}+3(-\frac{1}{2})-6=-2(\frac{1}{4})-\frac{3}{2}-6=-\frac{2}{4}-\frac{3}{2}-6=-\frac{2}{4}-\frac{6}{4}-\frac{24}{4}=\frac{-2-6-24}{4}=\frac{-32}{4}=-8$