Standard Equation: x²= 4py y²= 4px
vertical parabola horizontal parabola
axis y-axis x-axis
vertex (0,0) (0,0)
p is the focus of p>0 opens up p>0 opens right
the parabola
p<0 opens down p<0 opens left
focus (0,p) (p,0)
directrix y = -p x = -p
length of latus rectum 4|p| 4|p|

ex.
Graph x²= 6y

The standard equation is x² = 4py,
which implies a vertical parabola with the vertex at the origin and the axis is the y-axis.

4p = 6

P > 0, the parabola opens up and the focus is at (0, 3/2)
The directrix is the line y = -3/2

4|p| = 6, the end points of the latus rectum is (3, 3/2) and (-3, 3/2)

Graph y²= -16y

The equation is in the form: y² = 4px,
which implies a horizontal parabola with the vertex at the origin and the axis is the x-axis.

4p = -16
p = -4
p < 0, the parabola opens left and the focus is at ( -4,0).
The directrix is the line x = 4.
± 2p = ± 8; \ the end points of the latus rectum are points (-4, 8) and (-4, -8).