SOLUTION: an emergency flare is fired from a vehicle.its height ,h metres,is given by h(t)= -5t^2+35t+50,where t is the time in seconds. what is the maximum height reached by the flare and h

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: an emergency flare is fired from a vehicle.its height ,h metres,is given by h(t)= -5t^2+35t+50,where t is the time in seconds. what is the maximum height reached by the flare and h      Log On


   

Question 253497: an emergency flare is fired from a vehicle.its height ,h metres,is given by h(t)= -5t^2+35t+50,where t is the time in seconds. what is the maximum height reached by the flare and how long does it take to reach the maximum height? How long does it take the flare to hit the ground? i got the height at 85m
Found 2 solutions by richwmiller, Alan3354:
Answer by richwmiller(17219) About Me  (Show Source):
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
h(t)= -5t^2+35t+50,where t is the time in seconds. what is the maximum height reached by the flare and how long does it take to reach the maximum height? How long does it take the flare to hit the ground?
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Max height is the vertex of the parbola, at t = -b/2a
t = -35/-10 = 3.5 seconds
h(3.5) = -5*12.25 + 35*3.5 + 50
Max h = 111.25 meters
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It hits the ground at h = 0
-5t^2+35t+50 = 0
-t^2+7t+10 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B7x%2B10+=+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=%287%29%5E2-4%2A-1%2A10=89.

Discriminant d=89 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+89+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+89+%29%29%2F2%5C-1+=+-1.2169905660283
x%5B2%5D+=+%28-%287%29-sqrt%28+89+%29%29%2F2%5C-1+=+8.2169905660283

Quadratic expression -1x%5E2%2B7x%2B10 can be factored:
-1x%5E2%2B7x%2B10+=+%28x--1.2169905660283%29%2A%28x-8.2169905660283%29
Again, the answer is: -1.2169905660283, 8.2169905660283. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B7%2Ax%2B10+%29

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Ignore the negative number.