1. Warmup Alg 2 19 Apr 2012

2. Agenda Don't forget about resources on mrwaddell.net Section 9.2: Parabolas again! Non-Zero Vertex Completing the Square with Parabolas

3. Go over assignment from last class period

4. Section 9.2: Graphing a Parabola with a non-zero vertex

5. Vocabulary Parabola Focus Directorix Vertex Axis of symmetry A function with a SINGLE “squared” term Focus Directorix Vertex Axis of Symmetry Distances are the same!

6. Non-Zero Standard equation Standard FormVertexFocusDirectrix Vertical (x - h) 2 = 4p(y - k) (h, k)(h, k + p)y = k - p Horizontal (y - k) 2 = 4p(x - h) (h, k)(h + p, k)x = h - p Every point on a parabola is the same distance from the focus as from the directrix

7. What it looks like (x - h) 2 = 4p(y - k)

8. What it looks like (y - k) 2 = 4p(x - h)

9. Graphing (y - 3) 2 = 16(x + 2) Divide by 12 & find “p” So, p = 3 Vertex is (-2, 3) Focus is (-2+4, 3) Why? Directrix is x = -2 – 4 or x = -6 Why?

10. Vertex is (-2, 3) Focus is (2, 3) Directrix is x = -6

11. Graphing Divide by 20 & find “p” So, p = 5 Vertex is (-4, -2) Focus is (-4, -2+5) Why? Directrix is y = -2 – 5 or y = -7 Why? (x + 4) 2 = 20(y + 2)

12. Graphing Vertex is (-4, -2) Focus is (-4, 3) Directrix is y = -7

13. Simplest form All the equation does is translate the graph. Left or right is the number next to the “x” Up or down is the number next to the “y” But the sign changes! Keep it simple.

14. Completing the square y 2 – 10y + 5x + 57 = 0 We need to turn this into the standard form! Recall from back in Chapter 4, the method we used called Completing the Square.

15. Patterns in the “Genius Way” x 2 + 6x + 9 x 2 + 8x + 16 x 2 + 10x + 25 (x+3) 2 (x+4) 2 (x+5) 2 (x-7) 2 x 2 - 14x + 49 x 2 - 20x + ___ (x-__) 2 10 100 x 2 - 16x + ___ (x-__) 2 8 64 x 2 + bx + ___ (x+__ ) 2 b/2 (b/2) 2 x 2 + 7x + ___ (x+__) 2 7/2 49/4

16. Completing the square y 2 – 10y - 5x + 55 = 0 We take the “-10” (because the y is squared), divide by 2, and square the answer. -10/2 = -5 (-5) 2 = 25

17. Completing the square y 2 -10y -5x +55 = 0 Our genius numbers are -5 and 25 +5x – 55 +5x - 55 Move stuff y 2 -10y = 5x - 55Use the 25 to both+25 y 2 -10y +25 = 5x - 30Now we can factor (y - 5) 2 = 5(x – 6) Vertex is (6, 5) Focus is (6+5/4, 5) Directrix is x = 6 - 5/4 p = 5/4 (why?)

18. You Try! y 2 +8y -3x + 22 = 0 Our genius numbers are 4 and 16 +3x – 22 +3x - 22 Move stuff y 2 +8y = 3x -22Use the 16 to both+16 y 2 +8y +16 = 3x - 6Now we can factor (y +4) 2 = 3(x – 2) Vertex is (-4, 2) Focus is (-4+3/4, 2) Directrix is x = 6 - 3/4 p = 3/4 (why?)

19. You Try – Last one! x 2 +12x +8y -20 = 0 Our genius numbers are 6 and 36 -8y +20 Move stuff x 2 +12x = -8y +20Use the 36 to both+36 x 2 +12x +36 = -8y + 56Now we can factor (x +6) 2 = -8(y – 7) Vertex is (-6, +7) Focus is (-6, +7-2) Directrix is x = 7 - -2 p = -2 (why?)

20. Assignment Section 9.2:Handout