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## Parabolic Paranoia

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**Parabolic Paranoia**What are they good for?**What exactly is it?**• Parabola: “… is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface.” y(x) = x2**Where are all the parabolas?**• Suspension Bridges • Parabolic Antenna • Optical Lenses • Projectile Motion**Not Just A Hanging Chain**• Hanging Chain= Catenary, y = Cosh(x) - 1 • Hanging Chain & Weight = Parabola, • y = x2 • Hangin’ with Mr. Cooper= Awesome show from the 90s**Types of Bridges**• Truss • Suspension • Beam • Arch • Cantilever • Suspension • Cable-stayed • Truss**Suspension Bridges**• Tibetan architect and engineer ThangtongGyalpo was the first to use the “suspension bridge” idea circa 1430 • Main parts: • Towers • Deck • Anchorage • Cables • Stringers**Equation of a parabola**• y = Ax2 + Bx + C • (y-k)2 = 4p(x-h) • (h, k) : Vertex of the Parabola • p| : Distance from the Vertex • p : Direction Parabola Opens • (h+p, k) when p is positive or (h, k+p) when p is negative = Focus