Final answer:
The parabola given by the equation y = -9x² + 5x + 33 opens downward because the coefficient of the x² term is negative (-9).
Step-by-step explanation:
To determine whether the parabola opens upward or downward, we need to look at the coefficient of the x² term in the equation y = -9x² + 5x + 33. Since the coefficient is -9, which is negative, it means that the parabola opens downward. This is because the sign of the leading coefficient in a quadratic equation (which is the coefficient of the x² term) dictates the direction of the parabola's opening: a positive coefficient indicates an upward opening, while a negative coefficient indicates a downward opening.