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. (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.

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 $x = 0$ or $-16x+25=0$. Solving $-16x+25 = 0$ gives $16x=25$, so $x=\frac{25}{16}=1.5625\approx1.563$. The $x = 0$ intercept represents the time when the ball is initially kicked (at $t = 0$ seconds), and the non - zero $x$ intercept represents the time when the ball returns to the ground.

Answer:

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