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there are ___ parabolas that have a vertex (-3,-4) and pass through the point (-1,4)

  • math -

    We shall attempt to derive the Eq of an
    X-parabola and a Y-parabola using the
    given vertex and point.

    V(-3,-4), P(-1,4).

    Vertex Form: X = a(Y-K)^2 + h.
    X = a(4-(-4))^2 -3 = -1,
    64a - 3 = -1,
    64a = -1 + 3 = 2,
    a = 2/64 = 1/32.

    Eq: X = (1/32)(Y+4)^2 - 3.
    Therefore an X-parabola with the given
    vertex passes through the point given.

    Y = a(X-h)^2 + K.
    Y = a(-1-(-3))^2 - 4 = 4,
    4a - 4 = 4,
    4a = 8,
    a = 2.

    Eq: Y = 2(X+3)^2 - 4.
    Therefore, a Y-parabola with the given
    vertex passes through the givn point.

    Answer: 2 parabolas.

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