Question

Find the equation for the parabola with focus at (3, -3) and vertex at (3, 1).

Answer 1

The vertex form of a porabola is written \[y= a(x-h)^{2}+k\] if it opens up or down (if a is negative, it is down, if a is positive it is up)

OR is written \[x= a(y-k)^{2}+h\] if it opens left or right (if a is negative, it is left, if a is positive it is right)
(h,k) is the vertex and \[a=1/(4p)\], where p is the distance in the y direction "into the the parabola" of the focus of a parabola if the parabola open up or down, and p is the distance in the x direction "into the the parabola" of the focus of a parabola if the parabola opens left or right

use these formulas to find the equation