2. Lesson 10.2 Parabolas  Goal: Graph and write equations of parabolas

3. Quadratic Formula IF THEN

4. Objective - To solve quadratic equations using the quadratic formula. Quadratic Equation Quadratic Formula

5. ≈ 1.55 ≈ −0.22 x ≈ 1.55 or x ≈ -0.22

6. Solve. 3x 2 + 2x – 3 = 0 a = 3 b = 2 c = -3 x ≈ 0.72x ≈ −1.39

7. Solve. 5x 2 -2x – 1 = 0 a = 5 b = -2 c = -1

11. Creation of a Parabola  A conic section is a curve formed by the intersection of a plane a double-napped cone (Zoebel, 1997-2006)

12. Where are parabolas? (Internet Access is Required) They’re everywhere. Put arrow on icon and click. Click power point icon on task bar to continue with slide show after video is finished. (Part 1-They’re Out There!!!, 2008)

13. When you transform a function Inside the parentheses translates left and right (opposite of what you think) Outside the parentheses translates up and down (exactly what you think)

22. Definition of a Parabola (Larson, Boswell, Kanold & Stiff, 2005)

23. Parabolas  Parabolas with vertex at (0,0) and open up or down are in the form:

24. 4py  If positive, the parabola opens up  If negative, the parabola opens down

25. The Axis of Symmetry  For parabolas that open up or down, the axis of symmetry is the line x = the x-coordinate of the vertex.

26. The Focus  The focus is an ordered pair (x,y), and is INSIDE the parabola and on the axis of symmetry.

27. The Directrix  The directrix is a line that is perpendicular to the axis of symmetry and is always OUTSIDE the parabola.

28. 4p  4p is the number in front of the variable that has a coefficient of 1.  is the distance from the vertex to the focus and/or the distance from the vertex to the directrix.

29. The Vertex  The vertex lies halfway between the focus ( x, y) and the directrix (line).

30. Definition of a Parabola (Larson, Boswell, Kanold & Stiff, 2005)

31. #32 Identify the focus and directrix of the parabola.

32. opens up, with vertex at origin, to get the focus, plot the point 2 units inside the parabola and on the axis of symmetry, thus the focus is.

33. The directrix is perpendicular to the axis of symmetry and is also 2 units away from the vertex, so the equation of the directrix is