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Parabola Unit Intro Algebra I Chapter 9 Parabola Unit Intro Algebra I Chapter 9

Introduction n Quadratic Functions Non-linear u y = ax 2 + bx + c Introduction n Quadratic Functions Non-linear u y = ax 2 + bx + c u Physics Scenarios u n Graphs Symmetrical u Real-life applications u

Topics of Discussion n What parabolas look like Architecture u Sports u Natural u Topics of Discussion n What parabolas look like Architecture u Sports u Natural u Engineering u n Algebraic investigation Graphs u Vocabulary u

Parabolas in Architecture n Parabolas can be found in architecture They are added for Parabolas in Architecture n Parabolas can be found in architecture They are added for decorative purposes u They can also play a part in the support system for buildings u n Here are some examples

This one you know This one you know

Chicago Picasso Downtown Chicago Chicago Picasso Downtown Chicago

National Theatre Beijing, China National Theatre Beijing, China

Athens Olympic Stadium Athens, Greece Athens Olympic Stadium Athens, Greece

Qwest Field Seattle, Washington Qwest Field Seattle, Washington

Qwest Field, another view. Qwest Field, another view.

Sculpture House Evergreen, Colorado Sculpture House Evergreen, Colorado

Gateway Arch St. Louis, Missouri Gateway Arch St. Louis, Missouri

Tenerife Concert Hall Canary Islands, Spain Tenerife Concert Hall Canary Islands, Spain

Parabolas in Sports n n Objects that are thrown in air naturally follow a Parabolas in Sports n n Objects that are thrown in air naturally follow a parabolic curve Here are some examples

Falling Pong Ball Falling Pong Ball

Ping Pong ball rolling down a tube Ping Pong ball rolling down a tube

Basketball Free Throw Basketball Free Throw

A Golf Shot A Golf Shot

Another Golf Shot Another Golf Shot

Hammer Throw Hammer Throw

Motorcycle Racing Motorcycle Racing

Roller coasters Roller coasters

Parabolas in Nature n Parabolas occur naturally in the world n Here are some Parabolas in Nature n Parabolas occur naturally in the world n Here are some examples

Lamp Light bulbs Lamp Light bulbs

Rock Formations Rock Formations

Spinning Beaker Spinning Beaker

Rotates, and water reacts Rotates, and water reacts

More Water More Water

Iceberg Arch Iceberg Arch

Another one Another one

Rock Arch Rock Arch

Snow Thrower Snow Thrower

Engineering n Parabolas are used in structures for support They are found a lot Engineering n Parabolas are used in structures for support They are found a lot in bridges n Here a few examples n

Bridges…. . Bridges…. .

Golden Gate Bridge San Francisco, California Golden Gate Bridge San Francisco, California

Mackinac Bridge Mackinac, Michigan Mackinac Bridge Mackinac, Michigan

Ferrari 550 Maranello Ferrari 550 Maranello

Car Headlights Car Headlights

Satellite Dishes…. Satellite Dishes….

Satellite Engineering Satellite Engineering

Algebraic Side of Parabolas n n All parabolas are symmetrical around its axis of Algebraic Side of Parabolas n n All parabolas are symmetrical around its axis of symmetry Each parabola has either a maximum point or a minimum point called the vertex

Vertex and Axis of Symmetry n n n All parabolas can be reflected over Vertex and Axis of Symmetry n n n All parabolas can be reflected over its axis of symmetry The axis of symmetry always passes through the vertex Remember the spinning blue beaker?

Maximum and Minimums n Maximum or Minimum u u n n Left side - Maximum and Minimums n Maximum or Minimum u u n n 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/2 a where y=ax 2+bx+c

Graph of a parabola Graph of a parabola

Next Steps n n n We will find the vertex and axis of symmetry Next Steps n n n 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

Zeros - Where the graph crosses the x-axis Zeros - Where the graph crosses the x-axis