Question

A diver jumps off a platform at an initial upward velocity of 20 feet per second into the air above a pool. The height of the diver above the water after jumping can be represented by the function: h(t)=−16t2+20t

Use desmos to graph the function. Identify the x- intercept and interpret its meaning.



(2 points)
Responses

(1.25, 0); The horizontal distance of the length of the jump is 1.25 feet.
(1.25, 0); The horizontal distance of the length of the jump is 1.25 feet.

(0.625, 6.25); The diver will reach a maximum height of 6.25 feet 0.625 seconds after he jumps
(0.625, 6.25); The diver will reach a maximum height of 6.25 feet 0.625 seconds after he jumps

(1.25, 0); The diver will enter the water 1.25 seconds after he jumps
(1.25, 0); The diver will enter the water 1.25 seconds after he jumps

(0, 0); The diver jumps off the platform with an initial height of o feet.

Answer 1

To analyze the function \( h(t) = -16t^2 + 20t \), we need to find the x-intercept, which is the point where the height \( h(t) \) is equal to zero. This occurs when the diver hits the water.

Setting the function equal to zero:

\[
-16t^2 + 20t = 0
\]

Factoring out \( t \):

\[
t(-16t + 20) = 0
\]

This gives us:

1. \( t = 0 \) (the time at which the diver jumps)
2. \( -16t + 20 = 0 \) → \( t = \frac{20}{16} = 1.25 \)

Thus, the x-intercept is \( (1.25, 0) \).

**Interpretation:** The x-intercept \( (1.25, 0) \) means that the diver will enter the water 1.25 seconds after he jumps off the platform.

Therefore, the correct response is:

**(1.25, 0); The diver will enter the water 1.25 seconds after he jumps.**