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# Alg2 lesson 8-2

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### Alg2 lesson 8-2

1. 1. Vertex form (standard form) for the equation of a parabola y = a(x – h)2 + k x = a(y – k)2 + h Vertex: (h, k) Vertex: (h, k)Line of symmetry: x = h Line of symmetry: y = k
2. 2. Graph x = 2y2 + 8y + 9x = (2y2 + 8y )+9x = 2(y2 + 4y + 4) + 9 - 8x = 2(y + 2)2 + 1Vertex: (1, -2)Axis of symmetry: y = -2Opens to the right
3. 3. focus directrix
4. 4. latus rectum directrix
5. 5. y = a(x – h)2 + k focus 1 same distance 4a directrix latus rectum
6. 6. y = a(x – h)2 + k focus latus rectum length 1 directrix a
7. 7. Pg 422
8. 8. 4(y – 2) = (x + 3)2 y = a(x – h)2 + k4y – 8 = (x + 3)24y = (x + 3)2 + 84 4y = ¼ (x + 3)2 + 2a=¼h = -3k=2
9. 9. y = ¼ (x + 3)2 + 2vertex: (-3, 2)axis of symmetry: x = -3a=¼distance from vertex 1_to focus = 4(¼) = 1 Length of latusdistance from vertex rectum:to directrix = 1 1 = 4 units ¼
10. 10. 4x – 13 = y2 – 2y x = a(y – k)2 + h4x – 13 = (y2 – 2y +1) – 1 +13 +134x = (y – 1)2 + 124 4x = ¼ (y – 1)2 + 3
11. 11. x = ¼ (y – 1)2 + 3vertex: (3, 1)axis of symmetry: y=1a=¼distance from vertex 1_to focus = 4(¼) = 1 Length of latusdistance from vertex rectum:to directrix = 1 1 = 4 units ¼