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Analytic Goemetry

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Find the equation of the parabola with axis parallel to the x-axis and passing through (3/2,1),(5,0) and (-1,2).

  • Analytic Goemetry - ,

    In this case we don't know anything about the vertex, so we have to use the more general equation of the form
    x = ay^2 + by + c

    using (3/2 , 1) --- 3/2 = a + b + c
    using (5,0 ) ------ 5 = 0+0+c or c=5
    using (-1,2) ----- -1 = 4a + 2b + c

    from the 2nd we know c=5
    so in the first: a + b = -7/2 (#1)
    in the 3rd : 4a + 2b = -6 or 2a + b = -3 (#3)

    subtract #3 - #1 ----> a = 1/2
    back in #1 :
    1/2 + b = -7/2 ----- b = -4

    so equation is
    x = (1/2)y^2 - 4y + 5

    Check to see of all 3 points satisfy this equation.

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