SOLUTION: I really need help with the detail of solving this problem. Can someone please show me the step by step process in figuring out this problem? I have tried to calculate it man

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I really need help with the detail of solving this problem. Can someone please show me the step by step process in figuring out this problem? I have tried to calculate it man      Log On


   

Question 980221: I really need help with the detail of solving this problem. Can someone please show me the step by step process in figuring out this problem?
I have tried to calculate it many times and cannot for the life of me come up with the correct answer.
I am familiar with the quadratic formula but for some reason cannot get it to work for this problem.
“An object is thrown directly upward from a starting height of 25 ft and a starting velocity of 85 ft per second. The following function describes the height of the object with respect to the time, t.”
h(t) = -16t2 + 85t + 25
How long does it take before the object reaches the ground? Round you answer to
the nearest hundredths place.
The answer is 5.59.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
“An object is thrown directly upward from a starting height of 25 ft and a starting velocity of 85 ft per second. The following function describes the height of the object with respect to the time, t.”
h(t) = -16t2 + 85t + 25
How long does it take before the object reaches the ground? Round you answer to
the nearest hundredths place.
The answer is 5.59.
====================
Use ^ (Shift 6) for exponents.
h(t) = -16t^2 + 85t + 25
It hits the ground when h(t) = 0
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h(t) = -16t^2 + 85t + 25 = 0
Solve for t
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B85x%2B25+=+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=%2885%29%5E2-4%2A-16%2A25=8825.

Discriminant d=8825 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-85%2B-sqrt%28+8825+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2885%29%2Bsqrt%28+8825+%29%29%2F2%5C-16+=+-0.27942097313374
x%5B2%5D+=+%28-%2885%29-sqrt%28+8825+%29%29%2F2%5C-16+=+5.59192097313374

Quadratic expression -16x%5E2%2B85x%2B25 can be factored:
-16x%5E2%2B85x%2B25+=+%28x--0.27942097313374%29%2A%28x-5.59192097313374%29
Again, the answer is: -0.27942097313374, 5.59192097313374. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B85%2Ax%2B25+%29

=================
t = ~ 5.59 seconds
----
Ignore the negative solution.