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)

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

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

(1.25,0)
; The soccer ball will return to the ground 1.25 seconds after it has been kicked.

(0.781,9.766)
; The soccer ball will reach a maximum height of 9.766 feet 0.781 seconds after being kicked.

Answer 1

Factor: f(x) = −16x^2 + 25x = x(−16x + 25), so the roots are x = 0 and x = 25/16 = 1.5625 ≈ 1.563.

X-intercepts: (0, 0) and (1.563, 0). Interpretation: (0,0) is the kick at time 0; (1.563, 0) means the soccer ball returns to the ground about 1.563 seconds after being kicked.

(Therefore the correct choice is the one giving (1.563,0) with that interpretation.)