SOLUTION: A model rocket is launched from a height of 96 feet. The formula h=-16t^2+80t+96 describes the rockets height, h, in feet, t seconds after it was launched. How long will it take th

Question 27374: A model rocket is launched from a height of 96 feet. The formula h=-16t^2+80t+96 describes the rockets height, h, in feet, t seconds after it was launched. How long will it take the rocket to reach the ground?
Answer by mbarugel(146) (Show Source): You can put this solution on YOUR website!
This is a basic quadratic equation exercise. We want to find the t at which the rocket hits the ground. The fact that it hits the ground implies that the its height is now zero. So we must solve the equation:

We use the standard procedure:

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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=12544 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -1, 6. Here's your graph:

The two solutions are -1 and 6, but since time cannot be negative, the relevant solution is 6. The rocket hits the ground 6 seconds after it's launched.
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