Question

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

Vertex:(7,-6), Directrix: y=-25/4

Answer 1

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`