Quadratic Functions Project: Mathematics And The Arts

Name: Date: Period:Quadratic Functions Project: Mathematics and the Arts1.) Find an example of the graph of a quadratic function in a work of art orarchitecture. Make a copy of the picture of art/architecture.2.) Draw a coordinate graph system over the picture of the work of art orarchitecture that you’ve chosen (you may need to enlarge thequadratic 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 scaleclearly. (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 theequation 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 modelworks 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. Yourreport/poster should include information about the actual size of your artwork as well asthe 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 ofartwork/architecture. WARNING!!! Some pictures may appear to be parabolas but may not actually be realparabolas. If your artwork is not a true parabola, but is close, please make sure that youstate that in your project and presentation. Discuss the amount of error from a trueparabola.Project TimelineMust be completed & turned in by Monday, January 5th. Projects can be turned in -------------------------

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 inthis rubric on the day you present your project. It will be used to score your project.Rubric:CriteriaA coordinate graph was accuratelydrawn and labeled over a copy of theoriginal piece of parabola artwork. Anaccurate scale was included on thegraph, showing the relationshipbetween the picture size and the actualsize of the artwork/architecture.An original copy of the piece ofparabola artwork, without thecoordinate plane, was included.5 points were accurately labeled on thegraph of the parabola.A quadratic regression equation wasaccurately found and included a clearexplanation of the process used toobtain the equation.A 6th point on the graph was found andtested correctly in the quadraticregression equation, proving that theequation works. This equation andpoint-testing process proved that thepicture was indeed a true parabola orwas close. If it was not a true parabola,then the error factor was discussed. Allwork was shown.Results were presented in a well writtenreport or neat, organized poster.Poster/report includes at least 3interesting facts about the piece ofartwork/architecture.All sources were cited.(i.e. where did you get the picture? Anyother resources used?)TotalPoints possible222223215 pointsPoints earned

Example ProjectThe Eiffel Tower in Paris, FranceFull size image:Source: s-france.jpg

Enlarged Image:Source: 008/04/eiffel-tower.jpg3 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 5.5million people visit the tower every year.Source: re.asp

Coordinate Plane:yPredictionpoint tested inthe regressionequationCBDA-6Actual height: 986 ft tallHeight in this picture: 19 cm-4E-20246986/19 x8Scale:1 cm 51.9 ft

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 6.1297where the R2 value was equal to 0.9990458777. This value is very close to 1, but itisn’t exactly 1. Therefore, this shape is approximately a parabola, but it isn’t a perfectparabola.Error: 1- 0.9990458777 9.541223 E -4 0.0009541223Using the equation to make a prediction:I used my quadratic regression equation to predict the height of the parabolawhen x 4 on my coordinate plane.y -0.1278(4)2 0.0111(4) 6.1297 4.1293This answer has some error due to rounded numbers and the initial error inthe regression equation. However, it is approximately accurate and appearsto be true on the picture as well. (See labeled point on the picture)

Dec 23, 2014 · parabola artwork, without the coordinate plane, was included. 2 5 points were accurately labeled on the graph of the parabola. 2 A quadratic regression equation was accurately found and included a clear explanation of the process used to obtain the equation. 2 A 6th point on