Question

The Golden Gate Bridge sketched above is the seventh longest suspension bridge. The towers stand 748 feet above the water 4200 feet apart while supporting the deck 220 feet above the water. The sag from the tower to the lowest point on the suspension cables (the long cables running between the towers in a parabolic shape) is 500 feet. What is the model which describes the parabola made by the suspension cables.

Answer 1

To model this, we are going to set the lower point of the cable as the vertex of our parabola; that vertex will be the origin (0,0), so the line of symmetry of our parabola will be y-axis. Since the lower point of the cable is 220 feet above the see weather, the height of our function will be
`748-220=528`. Also, if the towers are 4200 ft apart, each tower will be half that distance to the line of symmetry of our parabola:
`(4200)/(2) =2100`. Now, we can infer that the height of the towers will the y-coordinates of our parabola, whereas the distance from each tower will the x-coordinates; therefore the points
`(-2100,528)` and
`(2100,528)` are on the graph of the parabola.

Now let use the basic form of the equation of a parabola:
`y=ax^(2)` to find
`a`:

`y=ax^(2)`

`528=a(2100)^(2)`

`a= (528)/(2100^(2) )`

Finally, lets replace
`a` in our previous equation to complete our model:

`y=ax^(2)`

`y= (528)/(2100^(2) ) x^(2)`

We can conclude that the model which describes the parabola made by the suspension cables is
`y= (528)/(2100^(2) ) x^(2)`.