Parabola Unit IntroAlgebra I

Chapter 9

Introduction

Quadratic Functions Non-linear y = ax2 + bx + c Physics Scenarios

Graphs Symmetrical Real-life applications

Topics of Discussion

What parabolas look like Architecture Sports Natural Engineering

Algebraic investigation Graphs Vocabulary

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

This one you know

Chicago PicassoDowntown Chicago

National Theatre Beijing, China

Athens Olympic StadiumAthens, Greece

Qwest FieldSeattle, Washington

Qwest Field, another view.

Sculpture HouseEvergreen, Colorado

Gateway ArchSt. Louis, Missouri

Tenerife Concert HallCanary Islands, Spain

Parabolas in Sports

Objects that are thrown in air naturally follow a parabolic curve

Here are some examples

Falling Ping 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

Parabolas occur naturally in the world

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

Parabolas are used in structures for support

They are found a lot in bridges

Here are a few examples

Bridges…..

Golden Gate BridgeSan Francisco, California

Mackinac BridgeMackinac, Michigan

Ferrari 550 Maranello

Car Headlights

Satellite Dishes….

Satellite Engineering

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

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?

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=ax2+bx+c

Graph of a parabola

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

Zeros - Where the graph crosses the x-axis