Hello, mattballer082!
These problems have the vertex at the origin.
There are two types:
. . . . . the parabola opens up or down: or
. . . . . the parabola opens right or left: or
is the distance from the Vertex to the Focus
. . and the distance from the Vertex to the Directrix.
Note: the curve always bends "around the Focus" and "away from the Directrix".
Find the equation of the parabola with the given features.
Graph the parabola.
1. Vertex (0,0), focus (0,3)
Make a sketch. Code:

* Fo(0,3) *
*  *
*  *
   o   
V(0,0)
Plot the Vertex and the Focus.
We know that the parabola bends around the Focus,
. . so we know its orientation: opens upward.
We use the form: .
We see that
. . Therefore, the equation is: .
2. Vertex (0,0), directrix x + 1 = 0
The vertex is at the origin; the directrix is the vertical line: Code:
:  *
:  *
: *
  +  o       
: *
:  *
:  *
x=1
Plot the Vertex and the Directrix.
We the know the parabola "bends away from the directrix"
. . so we know its orientation: opens right.
We use the form: .
We see that
. . Therefore, the equation is: .