Question:

Equations of parabolas?

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Write the equations of the parabolas with the following conditions:

a) with vertex (5,-3) and passing through (3,9)

b) passing through the points (-1,-6), (3,-12), and (2,-4.5)

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  1. (3,9) is above the vertex (5,-3), which fits an up-opening parabola. The general equation for an up-opening parabola is

    y-k = a(x-h)², a>0

    Plug in (3,9) and (5,-3):

    9+3 = a(3-5)²

    12 = a4

    a = 3

    Equation of the parabola:

    y+3 = 3(x-5)²

    http://www.flickr.com/photos/dwread/2816...

    Note that there is another solution: (3,9) is to the left of vertex (5,-3), which fits a left-opening parabola. The general equation for a left-opening parabola is

    x-h = a(y-k)², a<0

    Plugging in (3,9) and (5,-3):

    3-5 = a(9+3)²

    -2 = 144a

    a = -1/72

    Equation of the parabola:

    x-5 = (-1/72)(y+3)²

    http://www.flickr.com/photos/dwread/2816...

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