Graphing From Vertex Form

 

Step 1: Formula- y=a(x-h)2+k

 

Transformations:

"a"repersents sompression stretch

"h" repersents let and right movement

"k" repersents up and down movement

 

Step 2: Step Pattern y=x2

 

 

 

 

 

 

 

 

Step 3: Plot step pattern onto graph

 

Over one, up one

Over two, up four

 

 

 

 

 

 

 

 

 

 

 

 

 

Step 4: When given an equation without "a" value find the vertex

y=(x-1)2-4

 

-right one

-down four

 

Vertex=(1,-4)

 

(Note:The number in the bracket changes signs)

 

Step 5: Plot the vertex you found and do step pattern on it

 

 

 

 

 

 

 

 

 

 

 

 

 

Step 6: When given an equation with "a" value find the vertex

y=2(x+2)2-6

 

-left two

-down six

 

(Note:The number in the bracket changes signs)

 

Vertex=(-2,-6)

 

Step 7: Plot vertex

 

 

 

 

 

 

 

 

 

 

 

 

 

Step 8: Do not plot the regular step pattern, when given the "a" value you have to make changes to the step pattern

 

Multipy the step pattern with your "a" value

 

y=2(x+2)2-6

 

Step pattern= 1,4,9

-multiply 1,4,9 with "a" value (In this case the "a" value is 2)

New step pattern= 2,8,18

 

Step 9:Plot new step pattern

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Step 10: Analyzing the quadratic graph:

 

1.Vertex-find in equation.

 

2.Direction of opening- state weather the graph is opening up or down.

 

3.Max or Min Value-the "y" value in your vertex.

 

4.Axsis of symmetry-the "x" value in your vertex.

 

 

Conclutions

 

-Original step pattern for parabola is over one up one, over two up four, over three up nine(1,4,9).

 

-Vertex is where step pattern starts.

 

-The "a" value decides if the step pattern changes by multiplying the "a" value with the orignial step pattern.