\[
 - 3t^2  + 2t + 1 =  - 3\left( {t^2  - \frac{2}{3}t - \frac{1}{3}} \right) =  - 3\left[ {\left( {t - \frac{2}{6}} \right)^2  - \frac{4}{{36}} - \frac{1}{3}} \right] =  - 3\left[ {\left( {t - \frac{2}{6}} \right)^2  - \frac{{16}}{{36}}} \right] =  - 3\left[ {\left( {t - \frac{1}{3}} \right)^2  - \frac{4}{9}} \right] = 3\left[ {\frac{4}{9} - \left( {t - \frac{1}{3}} \right)^2 } \right]
\]