Answer:
Step-by-step explanation:
If you plot this point and the directrix on a coordinate plane, you can see that the directrix is 1/4 of a unit below the vertex. Since, by nature, a parabola opens in the direction opposite the directrix and "hugs" the focus, this is a positive x-squared parabola (meaning it opens upwards). The formula for this type of a parabola is, in vertex form,
[tex]4p(y-k)=(x-h)^2[/tex]
where p is distance (in units) between the vertex and the directrix and h and k are the coordinates of the vertex. For us, p = .25, h = 7, and k = -6. Filling in our formula:
[tex]4(.25)(y+6)=(x-7)^2[/tex]
Simplify the left side to
[tex]1(y+6)=(x-7)^2[/tex] which simplifies, in its entirety, to
[tex](x-7)^2-6=y[/tex]
