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Project - Modeling Quadratic Functions

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					HONORS ALGEBRA II                                    NAME ___________________________________

Optional Project:                              DATE _______________________PERIOD _____
Modeling Quadratic Functions in the Real World

This is not an extra credit assignment; it is an OPTIONAL project, which will be factored into
your marking period grade as a 25-point quiz, should you choose to complete the project.

Task:

In this activity you will select a natural or man-made arch, which can be modeled by a
quadratic function. You will identify the height and width of the arch, and use these
dimensions to identify the x-intercepts and vertex of the parabolic model. You will determine
a quadratic model for your arch and write it in Intercept Form, Vertex Form, and Standard
Form.

Your report must fulfill 2 goals:
(1)   Produce a professional report of research findings using technology
(2)   Demonstrate your understanding of quadratic functions


The Process:

1.      Choose an arch

        You may select any natural or man-made arch that is of interest to you. The arch must
        be a permanent object with fixed dimensions that can be verified. (For example,
        modeling the path of a football being kicked would not be appropriate, since the
        path of the football would change with each kick.)

2.      Collect data

        Select an image of the arch that illustrates its parabolic form. Determine the height
        and width of the arch, and look for information on its location and history. (Be sure to
        site all sources.)

3.      Determine a model

        Use the dimensions of the arch to determine a quadratic model. Use the Origin (0, 0)
        as one of the x-intercepts. The other x-intercept will correspond to the width of the
        arch. Determine the vertex using the average of the x-intercepts and the height of the
        arch. Write a quadratic model for your arch using all three forms of the quadratic
        function:

               Intercept Form :
               Vertex Form:
               Standard Form:
4.   Summarize your results

     Summarize your results in a well-written report using your choice of media (paper,
     poster, power point presentation, or other form). The report must have each of the
     following sections in the order given:

        o Name of Arch
        o Image
               Provide documentation of source
               Be sure the image is not copyright protected
        o Location
        o History
               If man-made, who designed/built it? When was it built? For what purpose?
               If natural, when was the arch discovered? By whom?
        o Dimensions
               You must provide documentation of the source of the information, so your
                 model can be verified.
        o Algebraic Model
               All three forms of the Quadratic Function must be listed
               You need not show your work
        o Sources
               Identify all sources used to gather information and images
               If your equations cannot be verified, you will receive no more than half
                 credit on this project.

5.   Evaulation

     You will be evaluated on your final report and presentation using the attached rubric.

Conclusion:

     This activity was designed to enable you to use technology to search for information
     and to present research results in a professional manner. In this activity you also
     furthered your investigation of least-squares regression by computing an equation to
     model your collected data. For many statisticians, this type of research and analysis is
     routine. Hopefully, you will find this to be a valuable lesson.

				
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