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)=−16x2+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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The x-intercepts of the function f(x) are the values of x where the function equals zero.

To find the x-intercepts, we set f(x) equal to zero and solve for x:

−16x^2 + 25x = 0

We can factor out x:

x(−16x + 25) = 0

So either x = 0 or -16x + 25 = 0.

Solving for x in the second equation:

-16x + 25 = 0
-16x = -25
x = 25/16

So the x-intercepts are (0, 0) and (25/16, 0).

Interpretation:

The x-intercepts represent the points where the soccer ball will return to the ground.

The x-coordinate of the first x-intercept, (0, 0), is 0. This means that the soccer ball will return to the ground immediately after it has been kicked.

The x-coordinate of the second x-intercept, (25/16, 0), is 1.563. This means that the soccer ball will return to the ground 1.563 seconds after it has been kicked.