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)

Question

Responses

(0.781,9.766); The soccer ball will reach a maximum height of 9.766 feet 0.781 seconds after being kicked.
left parenthesis 0.781 comma 9.766 right parenthesis ; 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.
left parenthesis 0 comma 1.563 right parenthesis ; 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.
left parenthesis 1.25 comma 0 right parenthesis ; The soccer ball will return to the ground 1.25 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

To analyze the situation, let's first understand the function \( f(x) = -16x^2 + 25x \), which represents the height of the soccer ball in feet after \( x \) seconds.

To find the x-intercepts (where the ball hits the ground), we need to set \( f(x) = 0 \):

\[ -16x^2 + 25x = 0 \]

Factoring out \( x \):

\[ x(-16x + 25) = 0 \]

Thus, we have:

1. \( x = 0 \) (when the ball is kicked)
2. \( -16x + 25 = 0 \) leads to \( 16x = 25 \Rightarrow x = \frac{25}{16} = 1.5625 \)

So, the x-intercepts are \( x = 0 \) and \( x = 1.5625 \) seconds.

The meaning of these x-intercepts:

• \( x = 0 \): This indicates the initial moment when the soccer ball is kicked.
• \( x = 1.5625 \): This indicates the moment when the soccer ball returns to the ground.

Thus the x-intercept we care about is approximately \( (1.563, 0) \), which means the soccer ball will return to the ground approximately 1.563 seconds after it has been kicked.

Based on the given answers, the correct response is:

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