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Parabola Unit Intro Algebra I Chapter 9
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Introduction Quadratic Functions Non-linear y = ax 2 + bx + c Physics Scenarios Graphs Symmetrical Real-life applications
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Topics of Discussion What parabolas look like Architecture Sports Natural Engineering Algebraic investigation Graphs Vocabulary
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Parabolas in Architecture Parabolas can be found in architecture They are added for decorative purposes They can also play a part in the support system for buildings Here are some examples
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This one you know
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Chicago Picasso Downtown Chicago
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National Theatre Beijing, China
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Athens Olympic Stadium Athens, Greece
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Qwest Field Seattle, Washington
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Qwest Field, another view.
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Sculpture House Evergreen, Colorado
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Gateway Arch St. Louis, Missouri
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Tenerife Concert Hall Canary Islands, Spain
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Parabolas in Sports Objects that are thrown in air naturally follow a parabolic curve Here are some examples
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Falling Ping Pong Ball
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Ping Pong ball rolling down a tube
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Basketball Free Throw
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A Golf Shot
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Another Golf Shot
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Hammer Throw
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Motorcycle Racing
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Roller coasters
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Parabolas in Nature Parabolas occur naturally in the world Here are some examples
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Lamp Light bulbs
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Rock Formations
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Spinning Beaker
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Rotates, and water reacts
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More Water
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Iceberg Arch
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Another one
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Rock Arch
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Snow Thrower
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Engineering Parabolas are used in structures for support They are found a lot in bridges Here are a few examples
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Bridges…..
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Golden Gate Bridge San Francisco, California
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Mackinac Bridge Mackinac, Michigan
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Ferrari 550 Maranello
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Car Headlights
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Satellite Dishes….
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Satellite Engineering
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Algebraic Side of Parabolas All parabolas are symmetrical around its axis of symmetry Each parabola has either a maximum point or a minimum point called the vertex
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Vertex and Axis of Symmetry All parabolas can be reflected over its axis of symmetry The axis of symmetry always passes through the vertex Remember the spinning blue beaker?
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Maximum and Minimums Maximum or Minimum Left side - leading coefficient is positive Right side - leading coefficient is negative The max or min always occurs at the vertex We find the vertex by -b/2a where y=ax 2 +bx+c
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Graph of a parabola
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Next Steps We will find the vertex and axis of symmetry of parabolas We will determine if the parabola opens up or down based on its equation We will find the roots or zeros of a quadratic equation
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Zeros - Where the graph crosses the x-axis
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