Math Help needed..please help.?

Question

The Golden Gate Bridge in San Francisco, is a suspension bridge. It is supported by a pair of cables that are parabolic in appearance. The cables are attached at either end to a pair of towers at points 152 m above the roadway. the towers are 1,280m apart and the cable reached its lowerst point when it is 4m above the roadway. Determine an algebraic expression that models the cable as it hangs between the towers. Transfer the data to a graph where the parabola lies below the x axis. Use the centre between the two towers as the y-axis...thanks..email me the graph if you can at [e-mail]..thanks for all your help.

Answer 1

First, I'll say that the true shape of the cable of a suspension bridge is a catenary, not a parabola. But going with the parameters of your problem, here's my answer:

The y-axis is centered between the two towers. They said that the graph should be below the x-axis, so I assume that means it is at the top of the two towers. The towers are 1280m apart, the bottom of the cable is 148m from the top. (152-4, since the cable ends up 4m above the roadway)

y = a x² + b

Now we just need to figure out some points and determine a and b.

The top of the left tower is at (-640, 0)
The bottom of the parabola is at (0, -148)
The top of the right tower is at (640, 0)

So:
y = a 0² + b = -148
b = -148

0 = a 640² - 148
a = 148 / 640²
a = 148 / 409600
a = 37 / 102400
a = 0.000361328125

So your function is:
y = 37 x² / 102400 - 148

A link to the graph is included below.

Answer 2

The first thing I thought of when reading through your question was it's a bad problem because the curve formed is a catenary, not a parabola... bandf is right on the money.

Working with the stated parabola, though, your equation will be of the form
y = a(x - h)² + k,
where (h, k) is the vertex of your parabola. With your given data, it's (0, 4).
[Note: the "k" on the end is arbitrary... I'm using it to have y equal to the height in meters above the roadway; the x-axis is the road, itself.]

Now your equation becomes
y = a·x² + 4. Find "a" and you're done.

You know that when x = 640 (half of the 1280 seaparating the towers),
y = 152. Substitute these values into your equation to solve for a.
152 = a·(640)² + 4
148 = a·409600
a = 148 / 409600 = 37 / 102400

Your final equation for the height of the cable becomes
y = (37 / 102400) · x² + 4.

To have the equation model the cable hanging down, subtract the 152 meters, leaving
y = (37 / 102400) · x² - 148.

Answer 3

its a symmetrical function so f(x)=ax^2 + c

and f(0)=-152 so c = -152

so f(1280)=0 = ax^2-152 and x = 1280 so solve for "a"

Answer 4

I think you should do your own homework.... its alot easier than you think. Draw a diagram yourself.