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 $f(x)=-16x^{2}+25x$. 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, 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.

Explanation:

Step1: Find x - intercepts

Set $f(x)=0$, so $-16x^{2}+25x = 0$.
Factor out an $x$: $x(-16x + 25)=0$.

Step2: Solve for x

Using the zero - product property, if $x(-16x + 25)=0$, then either $x = 0$ or $-16x+25 = 0$.
For $-16x+25 = 0$, we have $16x=25$, so $x=\frac{25}{16}=1.5625\approx1.563$.
The $x$-intercepts are $(0,0)$ and $(1.563,0)$. The $x = 0$ intercept represents the time when the ball is initially kicked (at time $t = 0$). The $x=1.563$ intercept represents the time when the ball returns to the ground.

Answer:

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