The equation $$ y=-3.5 x^{2}-0.5 x+65 $$ models the height of a ball in inches for each bounce. What is the best approximation for the height of the ball after the 3rd bounce? 7 in. 14 in. 32 in. 50 in.

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To find the height of the ball after the 3rd bounce using the equation:

$$ y = -3.5x^2 - 0.5x + 65 $$

where $$ x $$ represents the number of bounces, substitute $$ x = 3 $$:

$$
y = -3.5(3)^2 - 0.5(3) + 65
$$

Calculate each term step-by-step:

1. $$ 3^2 = 9 $$
2. $$ -3.5 \times 9 = -31.5 $$
3. $$ -0.5 \times 3 = -1.5 $$
4. Combine the results: $$ -31.5 - 1.5 + 65 = 32 $$

**Therefore, the best approximation for the height of the ball after the 3rd bounce is 32 inches.**

**Answer:** 32 in.
The height of the ball after the 3rd bounce is approximately 32 inches.

The equation \( y=-3.5 x^{2}-0.5 x+65 \) models the height of a ball in inches for each bounce. What is the best approximation for the height of the ball after the 3rd bounce? 7 in. 14 in. 32 in. 50 in.

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