Writing and Graphing Parabolas
Every parabola has the property that any point on it is equidistant from a point called the
focus (which lies on the axis of symmetry) and a line called the directrix ( which is
perpendicular to the axis of symmetry).
Standard Equation of a Parabola (Vertex at Origin)
The standard form of the equation of a parabola with vertex (0,0) is as follows.
Equation
Focus
Directrix
x2 = 4py
y2=4px
(0, p)
(p,0)
y= -p
x= -p
Graphing an equation of a Parabola
Graph the parabola- label the focus and directrix
x2=16y
Axis of Symmetry
Vertical (x=0)
Horizontal (y=0)
y2 = -8x
Writing the Equation of a parabola
1. Write an equation of the parabola with vertex (0,0) and focus( 4,0)
2. Write an equation of a parabola with vertex (0,0) and focus (0, ¼)
One of the largest radio telescopes has a diameter of 250 feet and a focal length of 50
feet. If the cross section of the radio telescope is a parabola, find the depth.