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Trig

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A parabola has its vertex on the graph of the line y=3x+1 and passes through (1,10). If it is the same size,?
shape, and direction as the graph of y=3x^2, find the equation (s) of all possible parabolas

Thanks!!!

  • Trig -

    let the parabola have equation
    y = 3(x-p)^2 + q
    (1,10) lies on it, so
    10 = 3(1-p)^2 + q

    also the vertex (p,q) lies on y = 3x+1
    thus:
    q = 3p + 1
    sub back into equation above

    10 = 3(1-p)^2 + 3p + 1
    10 = 3 - 6p + 3p^2 + 3p + 1
    3p^2 -3p -6 = 0
    p^2 - p - 2 = 0
    (p-2)(p+1) = 0
    p = 2 or p = -1

    if p=2, then q = 3(2) + 1 = 7
    and the parabola is y = 3(x - 2)^2 + 7

    if p = -1, then q = 3(-1) + 1 = -2
    and the parabola is y = 3(x+1)^2 - 2

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