SOLUTION: the height, h, of the rocket after t seconds is given by the equation h=-16t^2+120t+30. how long after the rocket is launched will it be 20 feet from the ground.

Question 644717: the height, h, of the rocket after t seconds is given by the equation h=-16t^2+120t+30. how long after the rocket is launched will it be 20 feet from the ground.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
the height, h, of the rocket after t seconds is given by the equation h=-16t^2+120t+30. how long after the rocket is launched will it be 20 feet from the ground.
.
Set h to 20 and solve for t:
h=-16t^2+120t+30
20=-16t^2+120t+30
0=-16t^2+120t+10
0=-8t^2+60t+5
0=8t^2-60t-5
solving for t using the quadratic formula yields:
t = {7.58, -0.08}
throw out the negative solution (extraneous) leaving:
t = 7.58 secs
.
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=3760 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 7.58242742918897, -0.0824274291889728. Here's your graph:

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