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.

(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 zeros are
x = 0 and x = 25/16 = 1.5625.

Interpretation: x is time (seconds). The ball is on the ground at t = 0 (initial kick) and again at t ≈ 1.5625 s (when it lands). So the nonzero x‑intercept ≈ (1.563, 0) is the landing time — this matches the third choice.

For completeness, the vertex (time of maximum height) is at
x = −b/(2a) = 25/(32) = 0.78125 s,
f(0.78125) = 9.765625 ft,
so the ball reaches about 9.766 ft at ≈ 0.781 s.

Graphically: a downward-opening parabola through (0,0) and (1.5625,0) with vertex (0.78125, 9.765625).