Lindblom Math and Science Academy



. Name: ________________________________ Date: _________ Period: __________

Quadratic Functions Project: Parabolas Everywhere

Objective: Why are we assigning this to you?

1) To recognize and identify parabolas in everyday life.

2) To model objects with parabolic shape with quadratic equations

Instructions: What you have to do!

1. Find 4 examples of the graph of a quadratic function with a camera anywhere around the city.

a. Your photos need to have an indentifying feature so I know you took the photo. Example: drawing a smile face on your finger with your initials and having it in the photo.

2. Choose 1 of your photos and draw a coordinate graph system over the picture. You may do this with tracing paper, graph paper, or on the computer. Mark the scale clearly. 

a. You may need to enlarge the quadratic part of the artwork to draw a set of coordinate axes.  If so, please include a copy of the original work of art or architecture as well

3. Find the coordinates of five points on your graph and place these five points on a clearly labeled table. Show your function fits by checking a 6th point.

4. Find the quadratic function that best models your image without the use of a regression.

a. To score highly you will need to explain in your report the steps you took to model this image with a quadratic function.

5. Write up your project in a REPORT section on your poster and to help we provided basic questions for you to answer. Simply answering the questions in the Minimum to earn a C but the quality and extension of each question can earn an A.

6. Discuss your project with the class in a 3 – 5 minute presentation. Make sure that your poster/paper includes at least 3 interesting facts related to your image you choose and has the other images you explored.

7. ** This project may be done electronically. You may capture images and map a quadratic equation to the screen. See at 1:00 minute for example.

Other information:

• All work will be completed outside of school.

• This project is to be completed independently. No two students can use the same piece of artwork/architecture or picture.

• WARNING!!! Some pictures may appear to be parabolas but may not actually be real parabolas. If your artwork is not a true parabola, but is close, please make sure that you state that in your project and presentation. Discuss the amount of error from a true parabola. (i.e St. Louis Arch)

Project Timeline

• M/T, 3/30: Project Assigned

• M/T, 4/13: Photos completed and brought to class for 15 points class participation

• Th/F, 4/23: Presentation day in class.

Project Idea Submission Form

Name: ___________________________ Date: ___________ Period: ______

Description of photo: _________________________________________________

Source: (where did you find it? )__________________________________________________

Project Title: ____________________________________________________

Use the following rubric as a “checklist” to help you as you complete your project. Please turn in this rubric on the day you present your project. It will be used to score your project.

Rubric:

|Criteria |Points possible |Points earned |

|4 original pictures of parabolas, without the coordinate plane included. |5 | |

|A coordinate graph was accurately drawn and labeled over a copy of 1 parabola. An |10 | |

|accurate scale was included on the graph, showing the relationship between the | | |

|picture size and the actual size of the parabola. | | |

|5 points were accurately labeled on the graph of the parabola. |10 | |

|A quadratic equation was accurately found and include in vertex form and standard |15 | |

|form. | | |

|A 6th point on the graph was found and tested correctly in the quadratic |15 | |

|regression equation, proving that the equation works. This equation and | | |

|point-testing process proved that the picture was indeed a true parabola or was | | |

|close. If it was not a true parabola, then the error factor was discussed. All | | |

|work was shown. | | |

|Report was well written to include how student found an appropriate a, h, k. |30 | |

|Please use the example as a guide to the quality of answers in your report. | | |

|Results were presented in a well written, neat, and organized poster. |5 | |

|Poster included at least 3 interesting facts about the photo and has all sections | | |

|of poster clearly labeled. | | |

|Presentation was clear, engaging, and between 3 -5 minutes in length. Discussion |10 | |

|of a, h, and k along with other aspects of quadratic functions were clear and | | |

|accurate. At least 3 interesting facts were discussed during the presentation. | | |

|Total |100 points | |

Example Project

The Eiffel Tower in Paris, France

Full size image:

[pic]

Source:

Enlarged Image:

[pic]

Source:

3 Interesting facts:

• The Eiffel tower is 986 feet tall and is constructed out of iron material.

• The Eiffel Tower was built in 1889 and was the tallest structure in the world until 1930.

• The tower was named after its designer and engineer, Gustave Eiffel, and over 5.5 million people visit the tower every year.

Source:

Coordinate Plane:

Actual height: 986 ft tall 986/19 (

Height in this picture: 19 cm

Finding the Quadratic Regression:

I chose 5 points on the graph with the following coordinates:

Point A: (-4, 4)

Point B: (-3, 5)

Point C: (1, 6)

Point D: (3, 5)

Point E: (5, 3)

I used these 5 points to calculate my quadratic regression equation in my calculator.

I found the following approximate equation:

y = -0.1278x2 + 0.0111x + 6.1297

where the R2 value was equal to 0.9990458777. This value is very close to 1, but it isn’t exactly 1. Therefore, this shape is approximately a parabola, but it isn’t a perfect parabola.

Error: 1- 0.9990458777 = 9.541223 E -4 = 0.0009541223

Using the equation to make a prediction:

I used my quadratic regression equation to predict the height of the parabola when x = 4 on my coordinate plane.

y = -0.1278(4)2 + 0.0111(4) + 6.1297

= 4.1293

This answer has some error due to rounded numbers and the initial error in the regression equation. However, it is approximately accurate and appears to be true on the picture as well. (See labeled point on the picture)

-----------------------

y

Prediction point tested in the regression equation

C

D

B

E

A

x

-6 -4 -2 0 2 4 6 8

Scale:

1 cm = 51.9 ft

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