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

Question

. Graph the function. Identify the x-intercept(s) and interpret its meaning.(1 point)
Responses

(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.

(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.

(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 find the x-intercepts of the function \( f(x) = -16x^2 + 25x \), we set \( f(x) = 0 \):

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

Factoring out \( x \):

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

This gives us two factors:

1. \( x = 0 \)
2. \( -16x + 25 = 0 \) → \( x = \frac{25}{16} \) = 1.5625 seconds

Thus, the x-intercepts are \( (0, 0) \) and \( (1.5625, 0) \).

Interpretation:

• The x-intercept \( (0, 0) \) represents the moment when the soccer ball is initially kicked from the ground (at time \( t = 0 \)).
• The x-intercept \( (1.5625, 0) \) means that the soccer ball will return to the ground approximately 1.5625 seconds after it has been kicked.

Given the provided options, the correct interpretation is:

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

(Note: the approximation of \( 1.5625 \) to \( 1.563 \) is acceptable depending on rounding.)