SOLUTION: The parabolic arch in the concrete bridge in
the figure must have a clearance of 50 feet above the water
and span a distance of 200 feet. Find the equation of the
parabola after
Algebra.Com
Question 856050: The parabolic arch in the concrete bridge in
the figure must have a clearance of 50 feet above the water
and span a distance of 200 feet. Find the equation of the
parabola after inserting a coordinate system with the origin
at the vertex of the parabola and the verticaly axis (point-ing upward) along the axis of the parabola.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The parabolic arch in the concrete bridge in the figure must have a clearance of 50 feet above the water and span a distance of 200 feet.
Find the equation of the parabola after inserting a coordinate system with the origin at the vertex of the parabola and the vertical axis (pointing upward) along the axis of the parabola.
:
from the description, the x intercepts are -100 and +100 and y intercept +50
Using the form ax^2 + bx + c = y, c = 50, b will cancel,
two equations for coordinates: x=100, y=0 and x=-100, y=0
100^2a + 100b + 50 = 0
-100^2a - 100 + 50 = 0
which is
10000a + 100b + 50 = 0
10000a - 100b + 50 = 0
----------------------- adding eliminates b, find a
20000a + 100 = 0
20000a = -100
a = -100/20000
a = -.005
the equation: y = -.005x^2 + 50, looks like this
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