Question
13. A soccer player kicks a ball with an initial velocity of 38 feet every second. The function f(x)=−16x2+38x
can be used to model the time the ball is in the air.
What is the meaning of the origin for this situation?(1 point)
Responses
After 38 seconds, the ball is at a height of 16 feet.
After 38 seconds, the ball is at a height of 16 feet.
After 16 seconds, the ball is at a height of 38 feet.
After 16 seconds, the ball is at a height of 38 feet.
At 0 seconds, the ball is at a height of 38 feet.
At 0 seconds, the ball is at a height of 38 feet.
At 0 seconds, the ball is at a height of 0 feet.
can be used to model the time the ball is in the air.
What is the meaning of the origin for this situation?(1 point)
Responses
After 38 seconds, the ball is at a height of 16 feet.
After 38 seconds, the ball is at a height of 16 feet.
After 16 seconds, the ball is at a height of 38 feet.
After 16 seconds, the ball is at a height of 38 feet.
At 0 seconds, the ball is at a height of 38 feet.
At 0 seconds, the ball is at a height of 38 feet.
At 0 seconds, the ball is at a height of 0 feet.
Answers
GPT-4o mini
In the context of the function \( f(x) = -16x^2 + 38x \), the variable \( x \) represents time in seconds, and \( f(x) \) represents the height of the soccer ball in feet. The origin of the graph, which is the point \( (0,0) \), represents the situation when \( x = 0 \).
At \( x = 0 \) seconds, substituting into the function gives:
\[ f(0) = -16(0)^2 + 38(0) = 0 \]
Therefore, the meaning of the origin (0,0) in this situation is:
**At 0 seconds, the ball is at a height of 0 feet.**
At \( x = 0 \) seconds, substituting into the function gives:
\[ f(0) = -16(0)^2 + 38(0) = 0 \]
Therefore, the meaning of the origin (0,0) in this situation is:
**At 0 seconds, the ball is at a height of 0 feet.**