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)

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

Answer 1

f(x) = −16x^2 + 25x is a downward-opening parabola.

- x-intercepts (roots): solve −16x^2 + 25x = 0 → x(−16x + 25) = 0, so x = 0 and x = 25/16 ≈ 1.5625.
Interpretation: the ball is on the ground at t = 0 and returns to the ground at t = 25/16 ≈ 1.563 seconds.

- Vertex (maximum): x = −b/(2a) = 25/(32) ≈ 0.78125 s, f(25/32) = 625/64 ≈ 9.7656 ft.
Interpretation: the ball reaches a maximum height of about 9.766 ft at t ≈ 0.781 s.

Therefore the first two statements are correct; the third (1.25, 0) is incorrect.