A parabola has its focus at (1,2) and its directrix is y = −2. The equation of this parabola could be...?

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  y =1/8(x -1)^2

Step-by-step explanation:

The vertex is halfway between the focus and directrix, so has y-coordinate (2-2)/2 = 0. The x-coordinate of the vertex is the same as that of the focus. The focus-vertex distance (p) is 2-0 = 2. Where the vertex is (h, k), the equation is ...

  y = 1/(4p)(x -h)^2 +k

For p=2, (h, k) = (1, 0), the equation of the parabola is ...

  y = 1/8(x -1)^2