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-intercepts and interpret its meaning. (1 point) Responses (1.25, 0) The soccer ball will return to the ground after it has been kicked (1.25, 0) The soccer ball will return to the ground 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, 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. (1.563, 0) 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.
The x-intercepts of the function can be found by setting f(x) equal to zero and solving for x:
-16x^2 + 25x = 0
Factor out an x:
x(-16x + 25) = 0
Set each factor equal to zero and solve for x:
x = 0 or -16x + 25 = 0
-16x + 25 = 0
-16x = -25
x = 25/16 = 1.563
So, the x-intercepts of the function are (0, 0) and (1.563, 0).
Interpreting the meaning, the x-coordinate of a point represents time, and the y-coordinate represents height. Therefore, the x-intercepts (0, 0) and (1.563, 0) represent the times when the soccer ball will return to the ground after being kicked. This means that at x = 0 seconds and x = 1.563 seconds, the soccer ball will hit the ground.