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Determine whether the parabola y=-9x²+5x+33 opens upward or downward.

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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.

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