Question 199175: Please help me solve this problem.
A parabolic arch has a span of 120 feet and a maximum height of 25 feet. Choose a suitable rectangular coordinate system and find the equation of the parabola. Then calculate the height of the arch 10, 20 and 40 feet from the center. Provide a sketch representing the situation and be sure it is clearly labled with coordinates.
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website! A parabolic arch has a span of 120 feet and a maximum height of 25 feet. Choose a suitable rectangular coordinate system and find the equation of the parabola. Then calculate the height of the arch 10, 20 and 40 feet from the center. Provide a sketch representing the situation and be sure it is clearly labled with coordinates.
The equation of the parabola with vertex (h,k) is
So the equation of the parabola with vertex (60,25) is
Since it goes through (0,0) we substitute that in:
So the equation of the parabola is
To find the height 10 feet from the center,
since the center is at 60, 10 feet from the
center is where x=50 and where x=70
we can either substitute  or 
Substituting 50,
 feet, approximately
To find the height 20 feet from the center,
since the center is at 60, 20 feet from the
center is where x=40 and where x=80
we can either substitute  or 
Substituting 40,
 feet, approximately
To find the height 40 feet from the center,
since the center is at 60, 40 feet from the
center is where x=20 and where x=100
we can either substitute  or 
 feet, approximately
Edwin
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