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Write 3y^2-x-12y+14=0 in the vertex form.

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Write 3y^2-x-12y+14=0 in the vertex form.

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The equation of the curve 3y^2 - x - 12y + 14 = 0 has to be written in the standard form.

3y^2 - x - 12y + 14 = 0 is the equation of a parabola. In the vertex form the equation is of the form (y - h)^2 = 4p(x - k) where (h, k) is the vertex.

3y^2 - x - 12y + 14 = 0

=> 3y^2 - 12y = x - 14

=> 3(y^2 - 4y + 4) = x - 14 + 12

=> 3(y - 2)^2 = x - 2

=> (y - 2)^2 = 4*(1/12)(x - 2)

This is the equation of a parabola with vertex (2, 2)

The vertex form of 3y^2 - x - 12y + 14 = 0 is (y - 2)^2 = 4*(1/12)(x - 2)

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