Warm-Up: February 22, 2012

1. Warm-Up: February 22, 2012 • Write the following equation in standard form (vertex form) • See sections 6-4 and 6-6 if needed. • Identify the vertex • Identify the axis of symmetry • In which direction does the parabola open?

2. Homework Questions?

3. Parabolas Section 8-2

4. Conic Sections • A conic section is any figure that can be obtained by taking a slice of a double cone.

5. Multiple Definitions of Parabola • The graph of a quadratic equation is called a parabola. • If a cone is sliced at the correct angle, the result is a parabola. • A parabola is the set of all points in a plane that are the same distance from a given point (called the focus) and a given line (called the directrix).

7. You-Try #2 • Graph • (Hint: look back at the warm-up)

8. Latus Rectum • Latin for “straight side” • The latus rectum is the line segment that passes through the focus and is perpendicular to the axis of symmetry. • Is parallel to the directrix • The length of the latus rectum is for the parabola with equation

9. Example 3a • Graph

10. You-Try #3a • Graph

11. Warm-Up: February 23/24, 2012 • Write in vertex form • Identify the vertex • Identify the axis of symmetry • Graph

12. Homework Questions?

13. Information About Parabolas

14. Other Textbooks • Vertical Directrix • p>0: opens right • p<0: opens left • Focus: (h + p, k) • Directrix: x = h - p • Axis of Sym.: y = k • Horizontal Directrix • p>0: opens upward • p<0: opens downward • Focus: (h, k + p) • Directrix: y = k - p • Axis of Sym.: x = h

15. Example 3b Find each of the following: • Vertex • Focus • Axis of symmetry • Directrix • Direction of opening • Length of latus rectum

16. You-Try #3b Find each of the following: • Vertex • Focus • Axis of symmetry • Directrix • Direction of opening • Length of latus rectum

17. Assignment • Page 424 #17-27 odd