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