# Quadratics in Nature and Architecture

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 Keywords: math, algebra, parabolas, Quadratics Subject(s): Math, Geometry, Algebra Grades 9 through 12 School: Haralson Co Cmty High School, Tallapoosa, GA Planned By: Gale Brown Original Author: Gale Brown, Tallapoosa
Students will learn that quadratics have real-world applications by discovery and research.
MM1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.
a. Represent functions using function notation.
b. Graph the basic functions f(x) = x^n where n = 1 to 3
c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes. (Also incorporates horizontal shifts from Math 2)
d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

1. After studying the characteristics and properties of quadratic functions, the students will be divided into groups. Each group will be given a Flip camera to capture quadratics in and around the school. The students will video each other describing the characteristics of the parabolas that they found, including the transformations that took place (i.e. reflections, shifts, etc.).

2. The students will return to class and choose two of the quadratics in their project to graph. The students will determine the equation of the quadratic and compare it to the parent graph, y=x^2 , confirming the transformations described in the video.

3. The groups will research other areas in nature and architecture where parabolas are found and either video these findings, take still shots or copy and paste research.

4. Each group will present their video, graphs and equations to the class in the form of a video or a PowerPoint that incorporates their video.

 Comments Students love getting out of their seats and the traditional classroom setting to learn. Many students today are kinesthetic learners due to the speed of their lives (i.e. Wii, XBox, texting, computing, sports) and we have to move our classrooms in that direction to reach them. Cross-Curriculum Ideas We have a film class that would love to take part in this project. I would love to see them produce math type films to use in our classrooms and this would be a great project to help get them moving that way. This could also be used in the Environmental Science class as they discuss symmetry in nature and other such topics. Follow-Up This would be an excellent opportunity for peer teaching in other classrooms. When students teach their peers, they make the topic more concrete for themselves. Materials: High, Math, Flash/USB Drives, Mice, LCD Monitors, Keyboards, Memory Cards, Batteries, Graphing, Point and Shoot, Flip Video, Slideshow, Integrating Technology Other Items: 1 Flip Camera Bundle, \$3995. each, total of \$3995.00