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Alg2 lesson 8-2
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Alg2 lesson 8-2

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  • 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. Graph x = 2y2 + 8y + 9
    x = (2y2 + 8y ) + 9
    x = 2(y2 + 4y + 4) + 9 - 8
    x = 2(y+ 2)2 + 1
    Vertex: (1, -2)
    Axis of symmetry: y = -2
    Opens to the right
  • 3. focus
    latus rectum
    directrix
    All points on the parabola are equidistant from the focus and the directrix.
  • 4. y = a(x – h)2 + k
    focus
    1 4a
    same distance
    directrix
  • 5. y = a(x – h)2 + k
    focus
    latus rectum
    1 a
    length =
    directrix
  • 6. Pg 422
  • 7. 4(y – 2) = (x + 3)2
    4y – 8 = (x + 3)2
    4y = (x + 3)2 + 8
    4 4
    y = ¼ (x + 3)2 + 2
    a = ¼
    h = -3
    k = 2
    y = a(x – h)2 + k
  • 8. y = ¼ (x + 3)2 + 2
    vertex: (-3, 2)
    axis of symmetry: x = -3
    a = ¼
    distance from vertexto focus = = 1
    distance from vertexto directrix = 1
    1_4(¼)
    Length of latus rectum:
    1 = 4 units¼
  • 9. 4x – 13 = y2 – 2y
    4x – 13 = (y2 – 2y )
    4x = (y – 1)2 + 12
    4 4
    x = ¼ (y – 1)2 + 3
    x = a(y – k)2 + h
    +1 – 1
    +13 +13
  • 10. x = ¼ (y – 1)2 + 3
    vertex: (3, 1)
    axis of symmetry: y = 1
    a = ¼
    distance from vertexto focus = = 1
    distance from vertexto directrix = 1
    1_4(¼)
    Length of latus rectum:
    1 = 4 units¼