SOLUTION: Please help me solve this equation: A ball is thrown upward with an initial velocity of 30 feet per second from a point that is 24 feet above the ground. The height h (in fe

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Question 173046: Please help me solve this equation:
A ball is thrown upward with an initial velocity of 30 feet per second from a point that is 24
feet above the ground. The height h (in feet) of the ball at time t (in seconds) after it is
thrown is
h= -16t^2 + 30t + 24
Find the time when the ball hits the ground.
Answer by KnightOwlTutor(293) About Me  (Show Source):
You can put this solution on YOUR website!
Set the equation to 0. When the ball hits the ground the distance is 0. Then use the quadratic formula.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case -16t%5E2%2B30t%2B24+=+0) has the following solutons:

t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2830%29%5E2-4%2A-16%2A24=2436.

Discriminant d=2436 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-30%2B-sqrt%28+2436+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%2830%29%2Bsqrt%28+2436+%29%29%2F2%5C-16+=+-0.604870334906633
t%5B2%5D+=+%28-%2830%29-sqrt%28+2436+%29%29%2F2%5C-16+=+2.47987033490663

Quadratic expression -16t%5E2%2B30t%2B24 can be factored:
-16t%5E2%2B30t%2B24+=+-16%28t--0.604870334906633%29%2A%28t-2.47987033490663%29
Again, the answer is: -0.604870334906633, 2.47987033490663. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B30%2Ax%2B24+%29
t=2.8