Quadratic Functions Project: Mathematics and the Arts
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. Other information:
● 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.
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:
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Criteria
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Points possible
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Points earned
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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
graph, showing the relationship
between the picture size and the actual
size of the artwork/architecture.
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2
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An original copy of the piece of parabola artwork, without the coordinate plane, was included.
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2
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5 points were accurately labeled on the
graph of the parabola.
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2
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A quadratic regression equation was
accurately found and included a clear
explanation of the process used to
obtain the equation.
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2
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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
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.
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2
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Results were presented in a well written
report or neat, organized poster.
Poster/report includes at least 3
interesting facts about the piece of
artwork/architecture.
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3
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All sources were cited.
(i.e. where did you get the picture? Any
other resources used?)
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2
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Total
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15 points
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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:
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)
Iused 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’ta 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)