Answer
Positive.
The parabola opens upward.
Work Step by Step
In the sum $at^2+bt+c$, the term $at^2$ prevails over the terms: $bt$ and $c$ for large values of $|t|$, that is, when $t→+∞$ or $t→-∞$
So, if $a\gt0$ the parabola open upward beacuse the term $ax^2$ is positive. If $a\lt0$ the parabola opens downward beacuse the term $ax^2$ is negative.
