Building a Bridge

Algebra 1 · Axiom Academy

Suspension-bridge cables form parabolas. Let's write the equation and find cable heights. Engineers are designing a suspension bridge whose main cable hangs in a parabola. They know: The bridge span (width) is 200 feet . The cable's lowest point is 10 feet above the deck. At each end of the span, the cable is 60 feet above the deck. Goal: find the equation of the cable, then its height at x = 50 and x = 75 feet from the center. The main cable, modeled with the origin at the center of the deck. Nice work — you modeled a suspension-bridge cable as a parabola and read real heights off it. Vertex form pays off: lets you write the equation the moment you know the vertex. One known point fixes the shape: substituting an end point gives the coefficient a = 0.005 . Then it's just evaluation: plug in any x to get the cable's height there. Parabolas aren't linear: three-quarters of the way out the cable is at 38.125 ft, not the 47.5 ft a straight line would give — the height climbs faster as you near a tower. The same idea sizes the cables and towers on real bridges like the Golden Gate.

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