Question

A soccer ball is kicked from the ground at an upward velocity of 25 feet per second. This situation can be represented by the function f(x)=−16x2+25x . Graph the function. Identify the x-intercept(s) and interpret its meaning.(1 point) Responses
A. (1.563,0) ; The soccer ball will return to the ground 1.563 seconds after it has been kicked.
B. (1.25,0) ; The soccer ball will return to the ground 1.25 seconds after it has been kicked.
C. (0,1.563) ; The soccer ball will return to the ground 1.563 seconds after it has been kicked.
D. (0.781,9.766) ; The soccer ball will reach a maximum height of 9.766 feet 0.781 seconds after being kicked.

Answer 1

To find the x-intercept(s) of the function, we set f(x) equal to 0 and solve for x:

-16x^2 + 25x = 0

Factoring out x, we get:

x(-16x + 25) = 0

Setting each factor equal to 0 gives us two possible x-intercepts:

x = 0 or -16x + 25 = 0

The first x-intercept is 0, which means the soccer ball starts at the ground (x = 0) before it is kicked.

To find the second x-intercept, we solve the equation -16x + 25 = 0:

-16x = -25
x = -25/-16
x ≈ 1.563

So the x-intercept is approximately (1.563, 0), and the correct interpretation is:

A. (1.563,0) ; The soccer ball will return to the ground 1.563 seconds after it has been kicked.