Parabolas
2
-2
4
-4
2
-2
4
-4
6
-6

The equation y = x2 is graphed above.

Quadratic equations (equations with 2 as the highest
power) are curved.  The curve is called a Parabola.
Click OK
Linear Equation
(Line Graph)
?
Quadratic Equation
(Parabola graph)
?
2
-2
4
-4
2
-2
4
-4
6
-6

Equation

of the

graph

y =x2

   Axis

     of

symmetry

Vertex

Other points

on the

parabola

Click OK
2
-2
4
-4
2
-2
4
-4
6
-6

Equation

of the

graph

?
y =x2

   Axis

     of

symmetry

?
Vertex
?

Other points

on the

parabola

?
2
-2
4
-4
2
-2
4
-4
6
-6
A     B          D     E
C
Which arrow
(A, B, C, D, or E)
shows the
axis of symmetry?

2
-2
4
-4
2
-2
4
-4
6
-6
    Axis of symmetry
x = -2
(           ,           )
What are the (x,y) coordinates
of the vertex?
The VERTEX
(turning point)
of the graph is always
on the axis of
symmetry.
2
-2
4
-4
2
-2
4
-4
6
-6
    Axis
     of
symmetry
?
Vertex
?
Step 1: Find the
Axis of symmetry

Step 2: Find vertex on
the axis of symmetry
( -2, -1 )
2
-2
4
-4
2
-2
4
-4
6
-6
    Axis of symmetry
x = -2
Vertex
Step 3: Plug x values
into the equation
of the parabola,

    y = x2 + 4x + 3

to plot other points
on the parabola.

( -2, -1 )
Click OK
2
-2
4
-4
2
-2
4
-4
6
-6
    Axis of symmetry
x = -2
?
?
Vertex
Step 4: Reflect (fold)
the other points over
the axis of symmetry.


Drag the reflected
points to the correct
location
( -2, -1 )
2
-2
4
-4
2
-2
4
-4
6
-6
    Axis of symmetry
x = -2
?
Vertex
( -2, -1 )
?
(Do you know the
axis of symmetry
equation from
vertex coordinates?)
You have
plotted 5 points
on the parabola
Step 2
Step 1
Step 3
Step 4
Use the axis of symmetry to find the VERTEX
?
Find the AXIS OF SYMMETRY (SUCH AS X = 3)
?
Plot 2 other points by plugging new x values in
the original equation (such as y = x2 + 8x - 20)
?
Reflect the 2 points over the axis of symmetry
for a total of 5 points (including the vertex)
?
Graphing Parabolas
The
      End
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