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Graphing Quadratic Functions and Conic Sections

Learn how to graph parabolas, circles, ellipses, and hyperbolas and solve applications involving them. Also, discover properties and rules for each type of conic section.

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Graphing Quadratic Functions and Conic Sections

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  1. Section 9.1 Quadratic Functions and Their Graphs

  2. Graph a parabola of the form . A OBJECTIVES

  3. Graph a parabola of the form . B OBJECTIVES

  4. Graph a parabola of the form . C OBJECTIVES

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

  6. Solve applications involving parabolas. E OBJECTIVES

  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 Chapter 9Section 9.1A Exercise #1

  14. Opens down.

  15. Section 9.2 Circles and Ellipses

  16. Find the distance between two points. A OBJECTIVES

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

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

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

  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 Chapter 9Section 9.2B Exercise #9

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

  27. Section 9.3 Hyperbolas and Identification of Conics

  28. Graph hyperbolas. A OBJECTIVES

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

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

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

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

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

  34. a = 3, b = 5

  35. Section 9.4 Nonlinear Systems of Equations

  36. Solve a nonlinear system by substitution. A OBJECTIVES

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

  38. Solve applications involving nonlinear systems. C OBJECTIVES

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

  40. Use the substitution method to solve the system.

  41. Use the substitution method to solve the system.

  42. Use the substitution method to solve the system.

  43. Section 9.5 Nonlinear Systems of Inequalities

  44. Graph second-degree inequalities. A OBJECTIVES

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