This is the concrete suspension bridge, in Mizen Head, Ireland.


external image images?q=tbn:ANd9GcQ5NRODPIdjE9451UXMBs1RpszO_tuQY7kFFPqLiOqY2N-bItC6pg
It is the only way to access this small area of land.
external image image1.JPG Bold means a repeating number.
History
It held one of the first telegraph stations and was where the first radio station in Ireland was located.
In 1847, when a boat crashed and sank on the shore of the island the local government decided to build a lighthouse. It then became much like Ellis Island, it was the first thing visitors and immigrants saw. The bridge was built in 1908, to provide easy access to visitors and workers. It is 172 feet across and 150 feet above sea level.
Equations
The standard form equation for the parabola is y=-0.004x^2+ 0.0119x +28.3409
I got the equation using quadratic regression.
The vertex form of the equation is y - 28.3409- 0.004(x)^2
The factored form of the equation is -(0.0632456x-5.41853)(0.0632456x-5.23037)
Axes
The parabola has 2 x intercepts, I know because it crosses the x axis twice. The place where the bridge touches the rock on the right side is the x axis (-82,0) the other x intercept is at (85,0). I had no way to measure where the y axis would be so I decided it would simply be in the middle.
Vertex
The vertex is the visible crossbeam in the middle. (0,28.3409) I used this picture as a guide. the bridge is 172 feet long. when I measured this picture, the bridge was 5.5 inches long. that means one inch is 31.27 feet. The crossbeam is 0.90625 of an inch from the x axis. 0.90625 * 31.27
28.3409 Therefore, the vertex is (0, 28.3409). The vertex form of this equation is y - 28.3409 - 0.004(x)^2 The vertex is a maximum. It is the tallest point on the bridge. The axis of symmetry is x=0
Intercepts
The y intercept of the parabola is the vertex, (0, 28.3409) The x intercepts are about (85,0) and (-82,0)
Discriminant
the discriminant of the equation is 0.453596155 it is not a perfect square.
This means the x intercepts should be irrational, but I have rounded them


New Mizen Head Footbridge
New Mizen Head Footbridge

Problem
The part of the bridge that is walked on is being replaced. The workers know the path is 11.27 feet from where the parabolic part of the bridge touches the rock.
Where on the parabolic part of the bridge do they have to put the path?
11.27=-0.004x^2+0.0119x+28.3409
0=-0.004x^2+0.0119x+17.0681
Quadratic Equation
-0.0119+-radical(0.0119^2-4*-0.004*17.0681)

2*-0.004
-63.85206008
66.82706008
Graph
parabola.png








Because I still cannot get a graph onto the page, I present this for your enjoyment.
external image tumblr_lyg07zJ8ci1qdz7owo2_400.gifPANDA AT THE DISCO!!!!!!!!!!!!!!!!!!!!!!!!