SOLUTION: You live near a bridge that goes over a river. The underneath side of the bridge is an arch that can be modeled with the function y = -0.000495x^2 + 0.619x where x and y are in fee

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: You live near a bridge that goes over a river. The underneath side of the bridge is an arch that can be modeled with the function y = -0.000495x^2 + 0.619x where x and y are in fee      Log On


   

Question 621746: You live near a bridge that goes over a river. The underneath side of the bridge is an arch that can be modeled with the function y = -0.000495x^2 + 0.619x where x and y are in feet. How high above the river is the bridge (the top of the arch)? How long is the section of bridge above the arch?
Answer by Alan3354(69443) About Me  (Show Source):
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You live near a bridge that goes over a river. The underneath side of the bridge is an arch that can be modeled with the function y = -0.000495x^2 + 0.619x where x and y are in feet. How high above the river is the bridge (the top of the arch)?
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The vertex is on the line x = -b/2a
x = -0.619/(-0.00099) = 61900/99
Sub that for x in the equation
--> y =~ 193.516 ft max
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How long is the section of bridge above the arch?
Find the 2 zeroes of the eqn. The straight line distance is the difference between the 2 zeroes.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -0.000495x%5E2%2B0.619x%2B0+=+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=%280.619%29%5E2-4%2A-0.000495%2A0=0.383161.

Discriminant d=0.383161 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0.619%2B-sqrt%28+0.383161+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280.619%29%2Bsqrt%28+0.383161+%29%29%2F2%5C-0.000495+=+0
x%5B2%5D+=+%28-%280.619%29-sqrt%28+0.383161+%29%29%2F2%5C-0.000495+=+1250.50505050505

Quadratic expression -0.000495x%5E2%2B0.619x%2B0 can be factored:
-0.000495x%5E2%2B0.619x%2B0+=+%28x-0%29%2A%28x-1250.50505050505%29
Again, the answer is: 0, 1250.50505050505. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.000495%2Ax%5E2%2B0.619%2Ax%2B0+%29

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One solution is 0, so the distance = 1250.5 feet