SOLUTION: Water in the tallest stream reaches a height of {{{h=20+84t-16t^2}}} feet at {{{t}}} seconds after leaving a nozzle on the fireboat. ***You can find the water's freatest height

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Water in the tallest stream reaches a height of {{{h=20+84t-16t^2}}} feet at {{{t}}} seconds after leaving a nozzle on the fireboat. ***You can find the water's freatest height      Log On


   

Question 40921: Water in the tallest stream reaches a height of h=20%2B84t-16t%5E2 feet at t seconds after leaving a nozzle on the fireboat.
***You can find the water's freatest height bu finding the vertext of the parabola for h=20%2B84t-16t%5E2***
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Water in the tallest stream reaches a height of h=20%2B84t-16t%5E2 feet at t seconds after leaving a nozzle on the fireboat.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case -16t%5E2%2B84t%2B20+=+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=%2884%29%5E2-4%2A-16%2A20=8336.

Discriminant d=8336 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-84%2B-sqrt%28+8336+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%2884%29%2Bsqrt%28+8336+%29%29%2F2%5C-16+=+-0.228178052628332
t%5B2%5D+=+%28-%2884%29-sqrt%28+8336+%29%29%2F2%5C-16+=+5.47817805262833

Quadratic expression -16t%5E2%2B84t%2B20 can be factored:
-16t%5E2%2B84t%2B20+=+-16%28t--0.228178052628332%29%2A%28t-5.47817805262833%29
Again, the answer is: -0.228178052628332, 5.47817805262833. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B84%2Ax%2B20+%29

Hope this helps.
Cheers,
Stan H.