1. Section 9.1 Quadratic Functions and Their Graphs

2. OBJECTIVES A Graph a parabola of the form.

3. OBJECTIVES B Graph a parabola of the form.

4. OBJECTIVES C Graph a parabola of the form.

5. OBJECTIVES D Graph parabolas that are not functions of the form

6. OBJECTIVES E Solve applications involving parabolas.

7. PROPERTIES For Parabola The vertex is at the origin and the y-axis is its line of symmetry.

8. PROPERTIES For Parabola If a is positive, the parabola opens upward, if a is negative, the parabola opens downward.

9. PROPERTIES For Parabola

10. PROPERTIES For Parabola

11. PROPERTIES For Parabola

12. PROPERTIES For Parabola

13. Practice Test Exercise #1 Chapter 9 Section 9.1A

14. Opens down.

15. Section 9.2 Circles and Ellipses

16. OBJECTIVES A Find the distance between two points.

17. OBJECTIVES B Find the equation of a circle with a given center and radius.

18. OBJECTIVES C Find the center and radius and sketch the graph of a circle when its equation is given.

19. OBJECTIVES D Graph an ellipse when its equation is given.

20. DEFINITION The Distance Formula

21. RULE Graphing Equation of a Circle

22. RULE

23. Graphing Equation of an Ellipse Centered at (0,0) If a and b are equal, the ellipse is a circle.

24. Graphing Equation of an Ellipse Centered at (h,k)

25. Practice Test Exercise #9 Chapter 9 Section 9.2B

27. Practice Test Exercise #10 Chapter 9 Section 9.2C

30. Section 9.3 Hyperbolas and Identification of Conics

31. OBJECTIVES A Graph hyperbolas.

32. OBJECTIVES B Identify conic sections by examining their equations.

33. RULES Graphing Equation of a Hyperbola with Center at (0,0)

35. RULES Graphing Equation of a Hyperbola with Center at (0,0)

37. Graphing Equation of a Hyperbola with Center at ( h,k )

38. Practice Test Exercise #16 Chapter 9 Section 9.3A

40. a = 3, b = 5

41. Section 9.4 Nonlinear Systems of Equations

42. OBJECTIVES A Solve a nonlinear system by substitution.

43. OBJECTIVES B Solve a system with two second-degree equations by elimination.

44. OBJECTIVES C Solve applications involving nonlinear systems.

45. Practice Test Exercise #18 Chapter 9 Section 9.4A

46. Use the substitution method to solve the system.

49. Section 9.5 Nonlinear Systems of Inequalities

50. OBJECTIVES A Graph second-degree inequalities.

51. OBJECTIVES B Graph the solution set of a system of nonlinear inequalities.

52. PROCEDURE 1. Graph each of the inequalities on the same set of axes. Graphing Nonlinear Inequalities

53. PROCEDURE 2. Find the region common to both graphs. The result is the solution set. Graphing Nonlinear Inequalities

54. Practice Test Exercise #22 Chapter 9 Section 9.5A

55. Vertex: (0, –1) x y 1 – 2 –1 – 2