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

ℎ
(
𝑡
)
=
−
16
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2
+
20
𝑡

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 initi

Answer 1

To analyze the function \( h(t) = -16t^2 + 20t \), we can find the x-intercepts by setting \( h(t) \) equal to zero:

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

Factoring out \( t \):

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

This gives us two solutions:

1. \( t = 0 \)
2. \( -16t + 20 = 0 \) → \( 16t = 20 \) → \( t = \frac{20}{16} = 1.25 \)

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

Interpretation of the x-intercepts:

• At \( t = 0 \): This means that the diver jumps off the platform at an initial height of 0 feet.

• At \( t = 1.25 \): This means that the diver will enter the water 1.25 seconds after he jumps.

Thus, the correct interpretation of the x-intercept \( (1.25, 0) \) is "The diver will enter the water 1.25 seconds after he jumps."