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"Parabolas Intro 2020"
Contributed by: Smith
2
-2
4
-4
2
-2
4
-4
6
-6
y =
y = 1
y = 3
Equations such as (y = some number) have horizontal lines for graphs.

Fill in the missing number for the bottom line.
2
-2
4
-4
2
-2
4
-4
6
-6
Equations such as y = mx + b
( y = a number times x + a number)
    also have lines for graphs.

These lines have a slope of   ½

y = ½x-1
y = ½x-3
Click OK
2
-2
4
-4
2
-2
4
-4
6
-6
Quadratic equations (equations with 2 as the highest
power) are curved.  The curve is called a Parabola.

The equation y = x2 is graphed above.

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)
points at 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

(The Axis of symmetry
     equation is the
 vertex' x-coordinate)
( -2, -1 )
?
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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