SOLUTION: s(t)=-16t^2+75t+407, Where t is the number of seconds elapsed. How long will it take the ball to reach a height of 450 feet above the ground? You may use the Quadratic formula or

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Question 148067: s(t)=-16t^2+75t+407, Where t is the number of seconds elapsed. How long will it take the ball to reach a height of 450 feet above the ground? You may use the Quadratic formula or completing the square. You might get two answers. Think about this: 450 feet may not be the highest elevation it gets. Unless 450 is the highest (think vertex), then it will reach that height as it comes up, reaches it again as it comes down. Round your answer(s) to the nearest tenth!
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
The problem provides the following equation:
s(t)=-16t^2+75t+407
.
They want to know the time(s) that the ball will be 450 ft high -- so, s(t)=450
.
So, now we have:
450=-16t^2+75t+407
Now, we solve for 't'.
.
450=-16t^2+75t+407
0=-16t^2+75t-43
.
Solving with the "quadratic equation" we get two solutions:
0.7 secs and at 4.0 secs
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B75x%2B-43+=+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=%2875%29%5E2-4%2A-16%2A-43=2873.

Discriminant d=2873 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-75%2B-sqrt%28+2873+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2875%29%2Bsqrt%28+2873+%29%29%2F2%5C-16+=+0.668738339592825
x%5B2%5D+=+%28-%2875%29-sqrt%28+2873+%29%29%2F2%5C-16+=+4.01876166040717

Quadratic expression -16x%5E2%2B75x%2B-43 can be factored:
-16x%5E2%2B75x%2B-43+=+-16%28x-0.668738339592825%29%2A%28x-4.01876166040717%29
Again, the answer is: 0.668738339592825, 4.01876166040717. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B75%2Ax%2B-43+%29