Question

Using the given information, give the vertex form equation for each parabola.

Answer 1

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,

$4p(y-k)=(x-h)^2$

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:

$4(.25)(y+6)=(x-7)^2$

Simplify the left side to

$1(y+6)=(x-7)^2$ which simplifies, in its entirety, to

$(x-7)^2-6=y$