A civil engineer is in charge of designing a bridge over a main shipping channel. The bracing of the bridge will form a parabola over the water as the diagram below shows. The engineer is thinking that a maximum height of 150 ft (at the center ) and a width of 700ft (at water level) will be wide enough. Below you will find the information and types of ships that will travel the river, and then decide if the engineer's design will meet the needs of the community. Things to remember: 1. We need at least 5ft of clearance from the top of the ship to the bridge for safety purposes
2. We need at least 10 ft of clearance on the sides of the ship for safety purposes
3. The equation for a parabola is y = a (x - h) ^ 2 + k where (h, k) is the vertex.

1) What are you going to use as a vertex for your parabola?
2) What will your equation be for this parabola?
3) The majority of the ships traveling the river come out of the water about 110 ft Can they safely travel the river? These ships are 175 ft wide and the water is deep enough for them to travel anywhere (left to right) on the river. How close to the sides of the bridge can the ship safely travel?
4) What is the maximum height of a ship that is 175 feet wide that could safely travel the bridge?

Design an overpass for highway 83 in the form of a parabolic arch that meets the requirements below. Keep in mind that we want to keep costs and heights to a minimum.

1. It must be at least 40 ft wide and 28 ft high at the center for a 2 lane highway.
2. The highway will have 12 ft wide lanes with one lane going in each direction.
3. We need to have at least 2 ft above a vehicle for safety.
Draw a picture and label the parts of the overpass.
a) What would you use for a vertex and what is your equation using y=a(x-h)^2+k?
b) Semi trucks will be the tallest vehicles traveling the highway, they reach heights of 14ft and will be traveling of centerCan they still pass through the underpass safely?
What would you suggest to someone hauling on highway 83 that has hay stacked 16 ft high? Give at least three options.