Question

A football player punts a ball. The path of the ball can be modeled by the equation y = –0.004x2 + x + 2.5, 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 football player will the ball land? Round to the nearest tenth of a foot.

125.0 ft

127.5 ft

247.5 ft

252.5 ft

Answer 1

Answer:the answer is 252.5

Explanation:

Answer 2

The answer is 252.5 ft

y = –0.004x² + x + 2.5
Let's take y = 0 and we'll get the quadratic equation:

–0.004x² + x + 2.5 = 0
The general formula for quadratic equation is:
ax² + bx + c = 0

a = -0.004
b = 1
c = 2.5


`x_(1,2) = \frac{-b+/- \sqrt{ b^(2)-4ac} }{2a} =\frac{-1+/- \sqrt{ 1^(2)-4*(-0.004)*2.5} }{2*(-0.004)} = (-1+/- √(1+0.04) )/(-0.008) = \\ =(-1+/- √(1.04) )/(-0.008) = (-1+/-1.02)/(-0.008)`


`x_1=(-1+1.02)/(-0.008) = (0.02)/(-0.008) = -2.5 \\ x_2=(-1-1.02)/(-0.008) = (2.02)/(-0.008) = 252.5`

Since distance cannot be negative (x1), the correct answer is x2 = 252.5 ft