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

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 where the ball will land, we need to set y (height) equal to 0 (since the ball will be on the ground) and solve for x (distance).

0 = -0.005x^2 + 0.7x + 3.5

We can rearrange this equation to make it easier to solve:

0.005x^2 - 0.7x - 3.5 = 0

Now, we can use the quadratic formula to solve for x:

x = (-(-0.7) ± √((-0.7)^2 - 4(0.005)(-3.5))) / (2(0.005))
x = (0.7 ± √(0.49 + 0.07)) / 0.01
x = (0.7 ± √0.56) / 0.01
x = (0.7 ± 0.748) / 0.01
x = 1.448 / 0.01 or x = -0.048 / 0.01
x = 144.8 feet or x = -4.8 feet

Since the ball cannot land -4.8 feet away from where it was hit, the ball will land approximately 144.8 feet from the batter, rounded to the nearest tenth of a foot.

So, the answer is D. 144.8 feet.