SOLUTION: An arch is in the shape of a parabola. It has a span of 320 meters and a maximum height of 16 meters. Find the equation of the parabola (assuming the origin is halfway between the

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Question 1198214: An arch is in the shape of a parabola. It has a span of 320 meters and a maximum height of 16 meters.
Find the equation of the parabola (assuming the origin is halfway between the arch's feet).
Determine the height of the arch 90 meters from the center.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
An arch is in the shape of a parabola.
It has a span of 320 meters and a maximum height of 16 meters.
Find the equation of the parabola (assuming the origin is halfway between the arch's feet).
:
Using the form ax^2 + bx + c
Using the origin as the midpoint: c = 16 and x = -160 and + 160 when y = 0
x=-160, y = 0
-160^2a - 160b + 16= 0
and
x=+160, y = 0
160^2a + 160b + 16 = 0
:
25600a - 160b + 16 = 0
25600a + 160b + 16 = 0
--------------------------Adding eliminates b, find a
51200a + 0 + 32 = 0
simplify divide by
1600a + 1 = 0
1600a = -1
a = -1/1600
a = -.000625
the equation
-.000625x^2 + 16 = 0
Looks like this

:
Determine the height of the arch 90 meters from the center.
x = 90
y = -.000625(90^2) + 16
y = -5.0625 + 16
y = 10.9375 meters (green line