Step 1: Teach
Make sure students have a graphing calculator. Demonstrate how to put the following problems in graphing calculator. Then complete problems with students.
Example 1
Graph the set of equations on the same screen in the standard viewing window. Describe any similarities and differences among the graph.
Enter the equations in the Y= list and graph in the standard viewing window (ZOOM 6).
Answer: Graphs are identical to , except the graph of is shifted up 2 units and the graph of is shifted down 2 units from the graph of .
Clear the Y= list before starting example 2.
Example 2
Graph the set of equations on the same screen in the standard viewing window. Describe any similarities and differences among the graph.
Answer: Graphs are identical to , except the graph of is shifted horizontally 3 units to the right and the graph of is shifted horizontally 2 units to the left from the graph of .
Clear the Y= list before starting example 3.
Example 3
Graph the set of equations on the same screen in the standard viewing window. Describe any similarities and differences among the graph.
Answer: All graphs open in the same direction. However, the graphs appear to have different widths. The graph of is narrower than the graph of . The graph of is wider than the graph of .
Step 2: Cooperative Groups
Divide the class into pairs. Then have students to work with their partner to complete problems 1-3.
How does each parameter affect the graph of ? Give an equation and explain the translation from the parent graph of .
- k
Partial answer: The k value changes the graph vertical
- h
Partial answer: The h value moves the graph horizontally
- a
Partial answer: The a value changes the width of the graph and it determines if the graph will open up or down.
Step 3:Practice
Examine each pair of equations and predict the similarities and differences in their graphs. Use your graphing calculator to confirm your predictions. Write a sentence or two comparing the two graphs.
- , +3
- ,
- ,