3. A batter strikes a baseball. The equation `y = -0.005x^{2} + 0.7x + 3.5` models its path, where x is the horizontal distance, in feet, the ball travels and y is the height, in feet, of the ball. How far from the batter will the ball land? Round to the nearest tenth of a foot.

Question

3. A batter strikes a baseball.  The equation `y = -0.005x^{2} + 0.7x + 3.5` models its path, where x is the horizontal distance, in feet, the ball travels and y is the height, in feet, of the ball.  How far from the batter will the ball land?  Round to the nearest tenth of a foot.
A. -4.8 feet
B. 4.8 feet
C. 145.9 feet
D. 144.8 feet

GPT 3.5 · Answer

To find how far from the batter the ball will land, we need to find the x-value where y = 0 (height is 0).

0 = -0.005x^2 + 0.7x + 3.5
0 = -0.005x^2 + 0.7x + 3.5
0 = -5x^2 + 700x + 3500
0 = -x^2 + 140x + 700

Using the quadratic formula, x = (-140 ± √(140^2 - 4(-1)(700))) / 2(-1)
x = (-140 ± √(19600 + 2800)) / -2
x = (-140 ± √22400) / -2
x = (-140 ± 149.666) / -2
x = (-289.666) / -2 or x = 9.666 / -2

Therefore, x = 144.8 or x = -4.8. Since x represents the distance traveled, the answer is 144.8 feet. So, the ball will land 144.8 feet from the batter.

The answer is D. 144.8 feet.