\[f(x) = \frac{1}{2}x^{2} + 3x\]
\[f\left( - \frac{1}{3} \right) = \frac{1}{2} \cdot \frac{1}{9} + 3 \cdot \left( - \frac{1}{3} \right) =\]
\[= \frac{1}{18} - 1 = - \frac{17}{18}.\]