SOLUTION: Suppose the height, h, in feet, of a trampolinist above the ground during one bounce is modelled by the quadratic function h(t) = -16t2 + 42t + 3.75 . For what period of time is th

Question 766965: Suppose the height, h, in feet, of a trampolinist above the ground during one bounce is modelled by the quadratic function h(t) = -16t2 + 42t + 3.75 . For what period of time is the trampolinist at least 22 ft above the ground? Round your answers to the nearest hundredth.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Suppose the height, h, in feet, of a trampolinist above the ground during one bounce is modelled by the quadratic function h(t) = -16t2 + 42t + 3.75 . For what period of time is the trampolinist at least 22 ft above the ground? Round your answers to the nearest hundredth.
.
Set h(t) to 22 and solve for t:
h(t) = -16t^2 + 42t + 3.75
22 = -16t^2 + 42t + 3.75
0 = -16t^2 + 42t - 18.25
0 = 16t^2 - 42t + 18.25
Applying the quadratic formula to the above, we get:
t = {0.55, 2.08}
.
Answer:
trampolinist is at least 22 ft from
0.55 to 2.08 seconds
.
Details of quadratic formula follows:
.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=596 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2.07540972598336, 0.549590274016644. Here's your graph:

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