Standard Equation: x<sup>2</sup>= 4py y<sup>2</sup>= 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 x^{2}= 6y

The standard equation is x^{2 }= 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 y^{2}= -16y

The equation is in the form: y^{2 }= 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.

Â± 2p = Â± 8; \ the end points of the latus rectum are points (-4, 8) and (-4, -8).