Pre calculus

The cable suspension bridge hangs in the shape of a parabola. The towers supporting the cable area is 600 lft apart and 200ft high. If the cable, at its lowest, is 40ft above the bridge at its midpoint, how high is the cable 50ft away(horizontally) from either tower?

-I’m confused pls help

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  1. Let's put all that information on the x-y grid
    with the vertex at (0,40)
    then the top of the towers are at (-300,200) and (300,200)
    then h = a(x-0)^2 + 40 = ax^2 + 40
    but (300,200) also lies on it, so
    200 = a(300)^2 + 40
    a = 160/90000 = 2/1125

    height = (2/1125)x^2 + 40

    "how high is the cable 50ft away(horizontally) from either tower?"
    you want x = 250
    find h

    btw, the cables on most suspension bridges hang according to a catenary, not a parabola.
    Google catenary.

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    Reiny

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