Bridges The New River Gorge Bridge in West Virginia is the world's largest steel single arch bridge. You can model the arch with the function
Know | Need | Plan |
---|---|---|
A function that models the arch and the vertical distance from the base of the supports to the water | The height of the arch above the support base and the length of the bridge above the arch | Find the vertex. The y-coordinate is the height of the arch above the support base. The x-coordinate is half the distance between the supports. |
How can you tell that the quadratic function has a maximum value?
Since
Step 1 Find the vertex of the arch.
The vertex is about (850, 360).
Step 2 Find the height of the arch above its supports.
The y-coordinate of the vertex is the height of the arch above its supports. The arch is about 360 ft above its supports.
Step 3 Find the height of the arch above the river.
The arch is about 360 ft + 516 ft = 876 ft above the river.
Step 4 Find the length of the bridge above the arch.
The x-coordinate of the vertex is half the length of the bridge above the arch. The length of that part of the bridge is about 850 ft + 850 ft = 1700 ft long.