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The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 600feet apart and 80 feet high. If the cables touch the road surface midway between the towers (vertex),find the equation for the height of the cable above the road. What is the height of the cable at a point150 feet from the center of the bridge?
I located the vertex at (0, 0). The top of one tower is at (300, 80)
So using x^2 = 4py I had
(300)^2 = 4p(80)
90000 = 320p
Dividing each side by 320, I determined that
p = 281.25
So x^2 = 4(281.25)y
x^2 = 1125y
At 150 ft from the center of the bridge:
(150)^2 = 1125y
22500 = 1125y
Dividing each side by 1125, I determined that
y = 20 ft