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

Question

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 function \( h(t) = -16t^2 + 20t \), we need to identify the x-intercept, which occurs when \( h(t) = 0 \).

To find the x-intercept(s), we can set the equation to zero:

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

Factoring out \( t \):

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

Thus, the solutions are:

\[ t = 0 \quad \text{or} \quad -16t + 20 = 0 \]

Solving the second equation:

\[ -16t + 20 = 0 \rightarrow 16t = 20 \rightarrow t = \frac{20}{16} = 1.25 \]

The x-intercepts are \( t = 0 \) and \( t = 1.25 \).

Interpretation of the x-intercepts:

1. \( (0, 0) \): This means the diver jumps off the platform at time \( t = 0 \) seconds with an initial height of 0 feet (the height of the water surface).
2. \( (1.25, 0) \): This means the diver will enter the water 1.25 seconds after jumping.

Conclusion:

Thus, the correct interpretation for the x-intercept of \( (1.25, 0) \) is:

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

This corresponds to the third response choice in your provided options.