1. **State the problem:** Determine whether the parabola given by the function $m(x) = 3x^2 + 9x - 5$ opens upward or downward. 2. **Recall the rule:** For a quadratic function $ax^2 + bx + c$, the parabola opens upward if $a > 0$ and downward if $a < 0$. 3. **Identify $a$:** Here, $a = 3$. 4. **Evaluate the sign of $a$:** Since $3 > 0$, the parabola opens upward. **Final answer:** The graph of the parabola opens upward.