1 / 20

Warmup Alg 2 19 Apr 2012

Warmup Alg 2 19 Apr 2012. Agenda. Don't forget about resources on mrwaddell.net Section 9.2: Parabolas again! Non-Zero Vertex Completing the Square with Parabolas. Go over assignment from last class period. Section 9.2: Graphing a Parabola with a non-zero vertex. Vocabulary.

martin-perez
Download Presentation

Warmup Alg 2 19 Apr 2012

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  6. Non-Zero Standard equation

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

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

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

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

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

  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 • y2 – 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+3)2 (x+4)2 (x+5)2 x2- 14x + 49 (x-7)2 (x-__)2 x2- 20x + ___ 10 100 (x-__)2 x2- 16x + ___ 8 64 (x+__ )2 x2 +bx + ___ b/2 (b/2)2 (x+__)2 x2+ 7x + ___ 7/2 49/4

  16. Completing the square • y2 – 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 Our genius numbers are -5 and 25 • y2 -10y -5x +55 = 0 +5x – 55 +5x - 55 Move stuff y2 -10y = 5x - 55 +25 +25 Use the 25 to both y2 -10y +25 = 5x - 30 Now we can factor p = 5/4 (why?) (y - 5)2 = 5(x – 6) Vertex is (6, 5) Directrix is x = 6 - 5/4 Focus is (6+5/4, 5)

  18. You Try! Our genius numbers are 4 and 16 • y2 +8y -3x + 22 = 0 +3x – 22 +3x - 22 Move stuff y2 +8y = 3x -22 +16 +16 Use the 16 to both y2 +8y +16 = 3x - 6 Now we can factor p = 3/4 (why?) (y +4)2 = 3(x – 2) Vertex is (-4, 2) Directrix is x = 6 - 3/4 Focus is (-4+3/4, 2)

  19. You Try – Last one! Our genius numbers are 6 and 36 • x2 +12x +8y -20 = 0 -8y +20 -8y +20 Move stuff x2 +12x = -8y +20 +36 +36 Use the 36 to both x2 +12x +36 = -8y + 56 Now we can factor p = -2 (why?) (x +6)2 = -8(y – 7) Vertex is (-6, +7) Directrix is x = 7 - -2 Focus is (-6, +7-2)

  20. Assignment • Section 9.2: Handout

More Related