
f4da03dc848cc09099f2b1690e3e6f24.ppt
- Количество слайдов: 49
Parabola Unit Intro Algebra I Chapter 9
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 Engineering u n Algebraic investigation Graphs u Vocabulary u
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
Chicago Picasso Downtown Chicago
National Theatre Beijing, China
Athens Olympic Stadium Athens, Greece
Qwest Field Seattle, Washington
Qwest Field, another view.
Sculpture House Evergreen, Colorado
Gateway Arch St. Louis, Missouri
Tenerife Concert Hall Canary Islands, Spain
Parabolas in Sports n n Objects that are thrown in air naturally follow a parabolic curve Here are some examples
Falling Pong Ball
Ping Pong ball rolling down a tube
Basketball Free Throw
A Golf Shot
Another Golf Shot
Hammer Throw
Motorcycle Racing
Roller coasters
Parabolas in Nature n Parabolas occur naturally in the world n Here are some examples
Lamp Light bulbs
Rock Formations
Spinning Beaker
Rotates, and water reacts
More Water
Iceberg Arch
Another one
Rock Arch
Snow Thrower
Engineering n Parabolas are used in structures for support They are found a lot in bridges n Here a few examples n
Bridges…. .
Golden Gate Bridge San Francisco, California
Mackinac Bridge Mackinac, Michigan
Ferrari 550 Maranello
Car Headlights
Satellite Dishes….
Satellite Engineering
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 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 - 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
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
f4da03dc848cc09099f2b1690e3e6f24.ppt