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.
(0, 0); The diver jumps off the platform with an initial height of o feet.
Question 7
5.

Answer 1

To analyze the height function of the diver represented by the equation \( h(t) = -16t^2 + 20t \), we recognize that this is a quadratic function.

### Finding the x-intercepts
To find the x-intercepts (where the diver enters the water), we set \( h(t) = 0 \):

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

Factoring out \( t \):

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

This gives us two solutions:

1. \( t = 0 \) (the moment the diver jumps off the platform)
2. Solving \( -16t + 20 = 0 \) gives:
\[
-16t = -20 \quad \Rightarrow \quad t = \frac{20}{16} = 1.25
\]

### Interpretation
The x-intercept at \( (1.25, 0) \) means that the diver will enter the water 1.25 seconds after jumping off the platform.

### Summary
Thus, to answer the question about the x-intercept:

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