Quadratic Functions Project: Mathematics and the Arts

Name: ______Date: ______Period: ______

1.) Find an example of the graph of a quadratic function in a work of art or architecture. Make a copy of the picture of art/architecture. 2.) Draw a coordinate graph system over the picture of the work of art or architecture that you’ve chosen (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). Mark the scale clearly. (You may do this with tracing paper, graph paper, or on the computer) 3.) Find the coordinates of five points on your graph and use these five points to find the equation of your quadratic regression function. Show the work for finding your equation. 4.) Find the coordinates of another point on your graph and check to make sure your model works for that point by substituting into your equation. Show this work too. 5.) Present your results in a well written report or neat, well organized poster. Your report/poster should include information about the actual size of your artwork as well as the scale that was used in your copy of the picture. Cite your sources. 6.) Discuss your project with the class in a 2 – 5 minute presentation. Make sure that your poster/paper includes at least 3 interesting facts related to your piece of artwork.

Other information:

 We will spend two days in class working on this assignment in the computer lab. All other 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.

 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.

Project Timeline  Monday, 2/23: Computer lab  Wednesday, 2/25: Computer lab  Thursday, 2/26: Artwork/architecture idea must be submitted by this date at the latest.  Monday 3/9 and Tuesday 3/10: Presentation days in class.

------Name: ______Date: ______Period: ______

Project Idea Submission Form (Detach this form and submit your project idea to Mrs. Friedman by 2/26)

Piece of Artwork/Architecture: ______

Source: (where did you find it? )______Name: ______Date: ______Period: ______

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 A coordinate graph was accurately drawn and labeled over a copy of the original piece of parabola artwork. An accurate scale was included on the 10 graph, showing the relationship between the picture size and the actual size of the artwork/architecture. An original copy of the piece of parabola artwork, without the 5 coordinate plane, was included. 5 points were accurately labeled on the 10 graph of the parabola. A quadratic regression equation was accurately found and included a clear 15 explanation of the process used to obtain the equation. A 6th point on the graph was found and tested correctly in the quadratic regression equation, proving that the equation works. This equation and point-testing process proved that the 15 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. Results were presented in a well written report or neat, organized poster. 30 Poster included at least 3 interesting facts about the piece of artwork/architecture. All sources were cited. (i.e. where did you get the picture? Any 5 other resources used?) Presentation was clear, engaging, and between 2 -5 minutes in length. At least 10 3 interesting facts were discussed during the presentation. Total 100 points Example Project The Eiffel Tower in Paris, France

Full size image: Source: http://www.visitingdc.com/images/eiffel-tower-paris-france.jpg

Enlarged Image:

Source: http://mrhiggins.net/algebra2/wp-content/uploads/2008/04/eiffel-tower.jpg

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: http://www.visitingdc.com/paris/eiffel-tower-picture.asp Coordinate Plane: y

Prediction point tested in the regression equation C B D A E

x -6 -4 -2 0 2 4 6 8

Scale: 1 cm = 51.9 ft 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)