# Math Help - Quadratic Funtion: Bridge Design

1. ## Quadratic Funtion: Bridge Design

The cables supporting a straight line suspension bridge are nearly parabolic in shape. Suppose that a suspension bridge is being designed with concrete supports 160 ft. apart and with vertical cables 30 ft. above road level at the midpoint of the bridge and 80 ft. above road level at a point 50 ft. from the midpoint of the bridge. How long are the longest vertical cables?

I got the equation: ${1\over50}(x-80)^2+30=0$ but not sure how I got the 1/50. Can anyone explain?

2. asuming the parabola is symmetrical to the y-axis, the basic equation is

$y = kx^2 + 30$

you have the point $(50,80)$ on the curve ...

$80 = k(50^2) + 30$

$k = \frac{1}{50}$