SOLUTION: A ball is thrown vertically upwars of 15 feet per second from a bridge that is 55 feet above the level of the water. The height h, in feet, of the ball above the water at time t in

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Question 479539: A ball is thrown vertically upwars of 15 feet per second from a bridge that is 55 feet above the level of the water. The height h, in feet, of the ball above the water at time t in seconds after it is thrown is h = 12t^2 + 20t - 48
Find the time when the ball strikes the water.
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
55=12t^2 + 20t - 48
12t^2 + 20t -103=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 12x%5E2%2B20x%2B-103+=+0) has the following solutons:

x%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=%2820%29%5E2-4%2A12%2A-103=5344.

Discriminant d=5344 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-20%2B-sqrt%28+5344+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2820%29%2Bsqrt%28+5344+%29%29%2F2%5C12+=+2.21261114708284
x%5B2%5D+=+%28-%2820%29-sqrt%28+5344+%29%29%2F2%5C12+=+-3.87927781374951

Quadratic expression 12x%5E2%2B20x%2B-103 can be factored:
12x%5E2%2B20x%2B-103+=+12%28x-2.21261114708284%29%2A%28x--3.87927781374951%29
Again, the answer is: 2.21261114708284, -3.87927781374951. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+12%2Ax%5E2%2B20%2Ax%2B-103+%29

t=2.21261114708284, -3.8792778137495
Throwing out the negative answer, we get t=2.21261114708284 seconds..