SOLUTION: The hight H that a certain arrow will reach T seconds after being shot directly upward is given by the formula H=112T-16Tē. what is the maximum hight for this arrow?

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Question 297446: The hight H that a certain arrow will reach T seconds after being shot directly upward is given by the formula H=112T-16Tē. what is the maximum hight for this arrow?
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
please use the quadratic section for these problems, this is not age related

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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aT%5E2%2BbT%2Bc=0 (in our case -16T%5E2%2B112T%2B0+=+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=%28112%29%5E2-4%2A-16%2A0=12544.

Discriminant d=12544 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-112%2B-sqrt%28+12544+%29%29%2F2%5Ca.

T%5B1%5D+=+%28-%28112%29%2Bsqrt%28+12544+%29%29%2F2%5C-16+=+0
T%5B2%5D+=+%28-%28112%29-sqrt%28+12544+%29%29%2F2%5C-16+=+7

Quadratic expression -16T%5E2%2B112T%2B0 can be factored:
-16T%5E2%2B112T%2B0+=+-16%28T-0%29%2A%28T-7%29
Again, the answer is: 0, 7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B112%2Ax%2B0+%29