1. Parabola Unit Intro Algebra I Chapter 9

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

3. Topics of Discussion What parabolas look like  Architecture  Sports  Natural  Engineering Algebraic investigation  Graphs  Vocabulary

4. 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

5. This one you know

6. Chicago Picasso Downtown Chicago

7. National Theatre Beijing, China

8. Athens Olympic Stadium Athens, Greece

9. Qwest Field Seattle, Washington

10. Qwest Field, another view.

11. Sculpture House Evergreen, Colorado

12. Gateway Arch St. Louis, Missouri

13. Tenerife Concert Hall Canary Islands, Spain

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

15. Falling Ping Pong Ball

16. Ping Pong ball rolling down a tube

17. Basketball Free Throw

18. A Golf Shot

19. Another Golf Shot

20. Hammer Throw

21. Motorcycle Racing

22. Roller coasters

23. Parabolas in Nature Parabolas occur naturally in the world Here are some examples

24. Lamp Light bulbs

25. Rock Formations

26. Spinning Beaker

27. Rotates, and water reacts

28. More Water

29. Iceberg Arch

30. Another one

31. Rock Arch

32. Snow Thrower

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

34. Bridges…..

36. Golden Gate Bridge San Francisco, California

37. Mackinac Bridge Mackinac, Michigan

39. Ferrari 550 Maranello

40. Car Headlights

41. Satellite Dishes….

43. Satellite Engineering

44. 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

45. 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?

46. 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

47. Graph of a parabola

48. 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

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