George Washington Bridge

Parabola Project

Elijah C.


The George Washington Bridge, opened
in 1931, connects New York and New
Jersey over the Hudson River. It was and
is an engineering marvel. As a suspension
bridge, it models a catenary curve. The
main span is 3,500 feet long and 212 feet
above the water, and the top of each of the
supporting towers is 604 feet above the
water. Draw and label a diagram of the
bridge. Using your graphing calculator, find
a quadratic regression that models the path
of the cable suspended between the two
towers. From the left end of your drawing,
where would support cables of length 300
feet be located on the bridge?

The George Washington bridge streches from Manhattan, New York to Fort Lee, New Jersey. The George Washington bridge was opened in 1931 over a course of 4 years. It is composed of an upper level and lower level and stands 604 feet tall. In history it has been used as a tool for suicide due to extensive pathways for pedestrians to walk on.
The bridge was built directly over the Hudson River which flows about
315 miles between New Jersey and New York. Cass Gilbert was the designer of this bridge in 1931 along with Othmar Ammann both famous architects. To this day it has gone down as being one of the most largely built bridges in history.

gw_bridge.jpg


Height of the Towers
(0,604)
(3500,604)
Vertex
(1750, 50)
y – 50= a (x - 1750)^2
604 – 50= a (3500-1750)^2
554=3062500a
0.0002
Vertex Form: y – 50= 0.0002 (x – 1750)^2
Standard Form: y= 0.0002x^2 – 0.7x + 662.5
Discriminant: 0.7^2 – (0.0002)(662.5)=0.49 – 0.53 = -0.04
The Vertex is (1750, 50) it is a minimum since the graph opens up at the center of the parabola.
The y-intercept of the graph is (0,604) which was the height of the tower.
The discriminant of my equation is 0.7^2 – (0.0002)(662.5)=0.49 – 0.53 = -0.04 and since the solution is negative it can’t be factored over integers and has no x- intercepts.