Question

13. A soccer player kicks a ball with an initial velocity of 38 feet every second. The functionf(x)=−16x2+38x%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A=%0D%0A−%0D%0A16%0D%0A%0D%0A2%0D%0A+%0D%0A38%0D%0A%0D%0A can be used to model the time the ball is in the air.%0D%0AWhat is the meaning of the origin for this situation?(1 point)%0D%0AResponses%0D%0A%0D%0AAfter 38 seconds, the ball is at a height of 16 feet.%0D%0AAfter 38 seconds, the ball is at a height of 16 feet.%0D%0A%0D%0AAfter 16 seconds, the ball is at a height of 38 feet.%0D%0AAfter 16 seconds, the ball is at a height of 38 feet.%0D%0A%0D%0AAt 0 seconds, the ball is at a height of 38 feet.%0D%0AAt 0 seconds, the ball is at a height of 38 feet.%0D%0A%0D%0AAt 0 seconds, the ball is at a height of 0 feet.

Answer 1

To understand the meaning of the origin (0,0) in the context of the function \( f(x) = -16x^2 + 38x \), we need to analyze what each part represents:

- The variable \( x \) typically represents time in seconds.
- The function \( f(x) \) represents the height of the soccer ball in feet at time \( x \).

Thus, the point \( (0,0) \) represents the situation at time \( x = 0 \) seconds, which is when the soccer ball is kicked. Specifically, the height of the ball at this time is \( f(0) = -16(0)^2 + 38(0) = 0 \) feet.

Now, let's look at the possible responses:

1. After 38 seconds, the ball is at a height of 16 feet.
2. After 16 seconds, the ball is at a height of 38 feet.
3. At 0 seconds, the ball is at a height of 38 feet.
4. At 0 seconds, the ball is at a height of 0 feet.

The correct response regarding the meaning of the origin (0,0) in this context is:

**At 0 seconds, the ball is at a height of 0 feet.**

This indicates that at the moment the soccer player kicks the ball (at time zero), the ball starts at ground level.