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)

(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.

(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.

Answer 1

f(x) = −16x^2 + 25x = x(−16x + 25) so the x-intercepts are x = 0 and x = 25/16 = 1.5625.
Thus the intercepts are (0, 0) and (1.5625, 0). Interpretation: t = 0 is the kick time; t ≈ 1.563 s is when the ball returns to the ground.

(For reference, the vertex is at t = 25/32 ≈ 0.78125 s with height f(0.78125) = 625/64 ≈ 9.7656 ft.)