Vertex form (standard form) for the equation of a parabola y = a(x – h)2 + k                     x = a(y – k)2 + h Vertex:...
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 =...
focus        directrix
latus rectum          directrix
y = a(x – h)2 + k                    focus                                                    1                           ...
y = a(x – h)2 + k                    focus     latus rectum      length       1                            directrix       a
Pg 422
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
y = ¼ (x + 3)2 + 2vertex: (-3, 2)axis of symmetry:     x = -3a=¼distance from vertex             1_to focus = 4(¼) = 1    ...
4x – 13 = y2 – 2y            x = a(y – k)2 + h4x – 13 = (y2 – 2y +1) – 1   +13                +134x = (y – 1)2 + 124      ...
x = ¼ (y – 1)2 + 3vertex: (3, 1)axis of symmetry:     y=1a=¼distance from vertex             1_to focus = 4(¼) = 1        ...
Alg2 lesson 8-2
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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

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