SOLUTION: Aubrey uses a slingshot to shoot a marble from a window. The height of the marble h(t) in feet at time t seconds is given by the function h(t)=-16t square -50t+164. How many second

Question 371009: Aubrey uses a slingshot to shoot a marble from a window. The height of the marble h(t) in feet at time t seconds is given by the function h(t)=-16t square -50t+164. How many seconds elapse before the marble hits the ground?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
h(t)=-16t square -50t+164
When it reaches the ground the "height" is zero
so, set h(t) to zero and solve for t:
0=-16t^2 -50t+164
0=16t^2 + 50t - 164
0=8t^2 + 25t - 82
Applying the "quadratic formula" we find that
t = {2, -5.125}
Throw out the negative answer leaving
t = 2 seconds
.
Details of quadratic to follow:
.

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=3249 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2, -5.125. Here's your graph:

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