Name:___________________ Partners______________Due Date: June 15, 2012 ALGEBRA II ART PROJECT CULMINATING ACTIVITY
(200 POINTS) Purpose: In this project, you will have an opportunity to mathematically translate graphical representation into its symbolic algebraic form. In other words, you will write equations that best describe a picture or drawing. In this activity, you will draw a picture, analyze each line and curve in the picture, and write their equations. Requirements: 1. Come up with original picture (either sketch or copied) that has been approved by me.
10 points 2. Trace sketch onto 8 ½” X 11” graph paper with a set of axes. 30 points 3. Determine the equations (at least 50) for each line / curve on the graph with restrictions. 75 points 4. Use equations to re-graph picture and check work (number each line that corresponds to each equation). 25 points 5. Write or Type equations and restrictions. 35 points 6. Create a final picture on white paper that is the image you worked on. 25 points Directions: 1. Using graph paper, draw a picture (sketch) which you would like to represent by using mathematical equations. Your picture can be based on a picture from a magazine, book or TV or it can be a picture you have made up on your own. Your picture should contain a VARIETY of types of equations such as lines, parabolas, hyperbolas, circles, exponentials, absolute values, .... 2. Further develop your rough sketch by finding the equations and the restrictions to the domain and/or range of your lines and curves. 3. Your FINAL PRODUCT will include the following items: a. A cover page b. The original picture that you decide to use c. The graph paper trace d. A typed or neatly written, numbered list of at least 50 equations along with the restrictions on the domain and/or range that correlate to your picture. e. All the work you did to get the equations and restricitons f. A copy of your regraphed picture on graph paper with the equations numbers written along each curve or line. g. A presentation quality, unnumbered picture traced from the regraph. Presentation quality means that the picture is neatly drawn and colored on unlined 8 ½ X 11" paper.
Evaluation: The project will be evaluated using the following criteria: • Completion of the steps outlined above • Creativity in using different types of equations • Degree of difficulty • Accuracy of the mathematics both in the equations and in the domains and ranges • Degree of variety of equations represented. (At least one of each type of conic section must be used… Parabola, Circle, Ellipse, Hyperbola) Example of Equations, Restrictions, and Regraph
Due Tuesday May 29th Draw a coordinate plane on graph paper with a drawn scale of -20 < x < 20 and -20 < y < 20. Now, draw the graphs for the given domains. EQUATIONS
RESTRICTIONS (domain and range)
y=
−1 2 ( x − 6 ) + 14 9
D [ 0,12]
y=
−1 2 ( x + 6 ) + 14 9
D [ −12, 0]
y = −2 x + 34
D [12,13]
y = 2 x + 34
D [ −13, −12]
x = 13
R [5,8]
x = −13
R [5,8]
y=
21 x − 16 13
D [ −13,13]
y =1
D [ −13, −10.5]
y =1
D [ −5,5]
y =1
D [10.5,13]
x = − y − 1 + 13
R [ 0, 2]
x = − y − 1 − 13
R [ 0, 2]
