Question

An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers are both 9 inches tall and stand 60 inches apart. Find the vertical distance from the roadway to the cable at a point on the road 12 inches from the lowest point of the cable.

Answer 1

First find the function of the form ax^2+bx+c...

We have the points (-30,9),(0,0),(30,9) so we know c=0 then we have:

900a-30b=9
900a+30b=9  adding these together

1800a=18, a=1/100 then 900a-30b=9 becomes:

9-30b=9

-30b=0 so b=0 so the parabola is just:

y(x)=x^2/100

y(12)=144/100=36/25

y(12)=1.44 in