2. Section 10-2 Pages 735-743 Introduction to Conics: Parabolas

3. Objectives I can write equations for parabolas in Standard Format I can graph parabolas by finding the key information for each I can complete the square to obtain vertex format

4. How to identify types of Conic Sections from General Form PARABOLASCIRCLES Either x or y is x and y are both squared but not squared with the both.same coefficient. ELLIPSESHYPERBOLASx and y are both squared with different squared, 1 is positive coefficients but the1 is negative. same signs.

5. Conic Sections A conic section is the intersection of a plane and a double cone.

6. Conical View

7. Parabolas (10-2) A Parabola is the set of all points in a plane that are equidistant between a fixed point (focus) and a line (directrix).

8. Real Parabolas Flashlights Headlights Mirrors Projectile Motion Satellite Dish Architecture

9. A Little Review You know the basic equation of any parabola as y = ax 2 + bx + c You can write this in vertex format and it becomes: y = a(x – h) 2 + k In that format, the vertex is (h, k); and the axis of symmetry is x = h In addition, if a > 0, then the parabola opened upwards, if a < 0 then the parabola opened down.

10. Review: Complete the Square Write y = 2x 2 + 12x + 14 in vertex format y = 2x 2 + 12x + 14 (Underline variables) y = 2 (x 2 + 6x) + 14 (Factor out the 2) y = 2 (x 2 + 6x + _____) + 14 - _______ y = 2 (x 2 + 6x + 9) + 14 – 18 y = 2 (x + 3)(x + 3) - 4 y = 2 (x + 3) 2 – 4 Vertex (-3, -4) Axis of Sym: x = -3 ; Opens: Upward since a > 0

11. A New Review The new equation we look at is x = ay 2 + by + c The new basic equation of a parabola is x = a(y – k) 2 + h In that format, the vertex is (h, k); and the axis of symmetry is y = k In addition, if a > 0, then the parabola opened Right, if a < 0 then the parabola opened Left.

12. Parabola A parabola is a set of points in a plane that are all the same distance from a fixed line called the directrix and a fixed point not on the line called the focus.

13. Vocabulary Any line segment that passes through the focus point with endpoints on the parabola is called a focal chord The perpendicular chord to the AOS is called the latus rectum(LR) Latus rectum

14. Key Concept The distance from Vertex Point to Focus Point is “p” This is also the same distance from Vertex Point to the Directrix Line

15. Parabolas

16. Where to find them… FOCUS: inside the parabola DIRECTRIX: outside of the parabola AOS: through the vertex, perpendicular to the directrix FOCAL CHORD (latus rectum): inside of the parabola

17. When graphing you MUST label… vertex focus directrix axis of symmetry endpoints of the focal chord

19. Homework WS 10-1