A soccer player kicks a ball with an initial velocity of 38 feet every second. The function

Question

f
⁡
(
x
)
=
−
16
x
2
2
+
38
⁢
x
can be used to model the time the ball is in the air.
What is the meaning of the origin for this situation?

A.
After 38 seconds, the ball is at a height of 16 feet.

B.
After 16 seconds, the ball is at a height of 38 feet.

C.
After 0 seconds, the ball is at a height of 38 feet.

D.
After 0 seconds, the ball is at a height of 0 feet.

Answer 1

To interpret the meaning of the origin (0,0) in the context of the function \( f(x) = -16x^2 + 38x \), we need to analyze what the variables represent.

In this function:

• \( x \) typically represents time in seconds.
• \( f(x) \) represents the height of the ball (in feet) at time \( x \).

The point (0,0) means:

• At time \( x = 0 \) seconds, the height \( f(0) = 0 \) feet.

This suggests that at the moment the soccer player kicks the ball (time = 0 seconds), the ball is at a height of 0 feet, meaning it is on the ground.

Therefore, the correct answer is:

D. After 0 seconds, the ball is at a height of 0 feet.