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find the equation of a parabola with vertex on the line y=2x, axis parallel to the x-axis and passing through (3/2, 1) and (3,4)

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  1. since the vertex is on the line y=2x, suppose it is at (h,2h). Then
    x = a(y-2h)^2 + h
    Now use the points to get
    a(1-2h)^2 + h = 3/2
    a(4-2h)^2 + h = 3
    solve to get
    x = -1/18 (y-7)^2 + 7/2
    x = 1/2 (y-2)^2 + 1

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