# Real World Parabola Proj.

### Created by Jaden Trowell & Miah Fear

## The Bean

Here's our picture from a distance. We chose "The Bean" located in Chicago, Illinois because it is an interesting real world parabola that intrigues people. It also has two parabolas, one on each side of the sculpture. Its real measurements are 66 ft long by 33ft high with an arch measuring 12 ft.

## The bean with axes

## The vertex and two other points

## Vertex & vertex form

- The vertex of the beans arch is located at (5,12) on the graph. The other two points are (9,4) & (16,4). The x axis represents the length in ft and the y axis is the height in ft.
- The equation in vertex form is y=(x-5)^2+12 found using the point (9,4).

## Work for Vertex Form

## Questions

*What does the height of the beans arch represent?**The height of the arch represents the y axis.*At the spot where the arch touches the ground, what is the relevance to the equation?**The spot where the arch touches the ground can represent the x axis and one of the zeros.*What is the maximum height of the arch*? *The maximum height of the arch is 12 ft.*How far away from the ground is the arch when it's at its maximum height?**The ground is about 9 ft away from the maximum height of the arch.*What is the domain related to the distance from the ground to the arch?**The domain is (9, 0) because 9 ft is the farthest measurement from the ground to the arch.*What is the range related to the height of the arch?** The range is (0, 12) because 12 ft is the absolute highest measurement of the arch.

## Recources

- Info on bean measurements - http://www.cityofchicago.org/city/en/depts/dca/supp_info/millennium_park_-artarchitecture.html#cloud
- Pictures - http://en.wikipedia.org/wiki/Cloud_Gate