[tex]x_{vertex}= \frac{-2}{2 \cdot 3}=- \frac{2}{6}= - \frac{1}{3} \\\\\\
y_{vertex}=3 \cdot \left(- \frac{1}{3} \right)^2+2 \cdot \left(- \frac{1}{3} \right)+1=3 \cdot\frac{1}{9} - \frac{2}{3} +1=\frac{1}{3} - \frac{2}{3} +1= \frac{2}{3} \\ \\ \\ \boxed {\text {Answer:} \ \left(- \frac{1}{3}; \frac{2}{3} \right)}[/tex]
