Graphing parabola
Using the method of squares
The parabola we areto graph are having origin as
our vertex
Compare the equationto x2=4py
for a parabola with y-axis as its axis of symmetry
Compare the equationto y2=4px
for a parabola with x-axis as its axis of symmetry
In graphing parabolawe use squares to asses
our graphing
Parts of a parabolaFocus: F(0,p)
for a parabola of the form x2=4py
Use the six squares whose sides equal to
2p
Sample: x2=6y Solution: compare the problem , x2 =6y to x2 = 4py
4py=6y by transitive property, and p=1.5 by dividing
4y to both sides
From the results
Focus (0, 1.5) or (0,p)Length of latus rectum 4p or 6 units
Vertex (0,0)Directrix: y= -1.5 or y= -p
We draw the graph using six squares
with sides equal to 2p or 3 units
x2 =6y length of latus rectum
6
1
2 5
4
3 Vertex (0,0)
Directrix: y= -1.5
The ordered pairsThe red colors on previous slide are the
points on the parabola.The ordered pairs are found on the vertex of
the squares, upper vertex of squares 1,3,4 and 6.
The lower portion which is the origin is found on the sides of squares 3 and 4.
Sample 2: y2 =8xIn this case the graph has an axis of symmetry which is the x- axis , and the directrix is at the left side of the origin
Solution y2= 8x will be compared to
y2=4px, which yields p=2
The squares
Length of latus rectum
directrix
Vertex (0,0)
The red colored are the points on the parabola that passes the edges of the squares
All the squares have the sides of 4 units
Thank you for viewing
Virgilio Rollon ParageleTomas Cabili National High School