Quadratics Part 1
 y = a(x - h)2 + k

Enter a = 1, h = 0, k = 0   
gives y = 1(x - 0)2 + 0  or y = x2
Click Graph, then Click Store.
Use this graph to compare 

1 . Enter a = 1, h = 0, k = -2 

Predict which way the graph will SHIFT?
Up Left None
Down

Right
Now click Graph.

2. Enter a = 1, h = 0, k = 2 

Predict which way the graph will SHIFT?
Up Left None
Down

Right
Now click Graph.

3. Enter a = 1, h = 0, k = -3/2 

Predict which way the graph will SHIFT?
Up Left None
Down

Right
Now click Graph.
Quadratics Part 2
 y = a(x - h)2 + k

Enter a = 1, h = 0, k = 0   
gives y = 1(x - 0)2 + 0  or y = x2
Click Graph, then Click Store.
Use this graph to compare 

1 . Enter a = 1, h = 2, k = 0 

Predict which way the graph will SHIFT?
Up Left None
Down

Right
Now click Graph.

2. Enter a = 1, h = -2, k = 0 

Predict which way the graph will SHIFT?
Up Left None
Down

Right
Now click Graph.

3. Enter a = 1, h = 4/3, k = 0 

Predict which way the graph will SHIFT?
Up Left None
Down

Right
Now click Graph.
Quadratics Quick Quiz
Without graphing predict which way the graph will shift from  y = x2

 1.  y = (x + 2)2  
Predict which way the graph will SHIFT?
Up 2 Left 2 None
Down 2

Right 2
Verify with grapher

 2.  y = x2 + 3
Predict which way the graph will SHIFT?
Up 3 Left 3 None
Down 3

Right 3
Verify with grapher

 3.  y = (x - 3)2  
Predict which way the graph will SHIFT?
Up 3 Left 3 None
Down 3

Right 3
Verify with grapher

 4.  y = x2 - 1
Predict which way the graph will SHIFT?
Up 1 Left 1 None
Down 1

Right 1
Verify with grapher
Quadratics Part 3
 y = a(x - h)2 + k

Enter a = 1, h = 0, k = 0   
gives y = 1(x - 0)2 + 0  or y = x2
Click Graph, then Click Store.
Use this graph to compare 

1 . Enter a = 1/2, h = 0, k = 0 

Predict which way the graph will CHANGE?
Vertical Shrink - widen None
Vertical Stretch - narrow
Now click Graph.

2. Enter a = 2, h = 0, k = 0 

Predict which way the graph will CHANGE?
Vertical Shrink - widen None
Vertical Stretch - narrow
Now click Graph.

3. Enter a = -1, h = 0, k = 0 

Predict which way the graph will CHANGE?
Reflect across  x -axis None
Reflect across  y -axis
Now click Graph.

4. Enter a = 1/10, h = 0, k = 0 

Predict which way the graph will CHANGE?
Vertical Shrink - widen None
Vertical Stretch - narrow
Now click Graph.

5. Enter a = -4, h = 0, k = 0 

Predict which way the graph will CHANGE?
Reflect across  x -axis None
Reflect across  y -axis
Now click Graph.
Quadratics Altogether
Predict the following shifting, then verify using grapher.
y = 2(x - 3)2  + 4
y = -2(x + 3)2  - 4
y = 1/4(x + 2)2  + 1
y = -4(x - 1)2  -  2
y = (x - 2/5)2  - 1/5
 
Quadratics Part 4
 y = a(x - h)2 + k
The vertex is the point (h,k)
If a > 0 , then the vertex is the lowest point of the graph.  (opens upward)
If a < 0 , then the vertex is the highest point of the graph.  (opens downward)

Examples: 
Quadratic Vertex
y = (x - 1/2)2  + 3/5 (1/2, 3/5)
y = -2 (x + 3)2  - 4 (-3,-4)
y = 3(x + 1)2   (-1,0)
y = -2x2  - 4 (0,-4)
y = 2 (x - 3)2  + 4 (3,4)

Tutorials and Applets by
Joe McDonald
Community College of Southern Nevada