Lesson 2

Explore

 

In Lesson 1 you created three general rules about the effects of a, p, and q on y = a(x − p)2 + q. In Try This 1, just now, you identified a rule that relates the vertex to y = a(x − p)2 + q. Go to your course folder and add your new rule to the three rules you identified in Lesson 1, Share 1, question 4.
 
You are now going to create one more rule, your fifth rule in total. This rule will help you create a sketch of a quadratic function.

 

Try This 2

1. Use Quadratic Function (Vertex Form) to explore how the variables a and q can be used to determine the number of x-intercepts in a given quadratic function. You may use a table like the one shown to record your observations.
   
   
    
   
   
   
    

   a	q	Sketch	Number of x-Intercepts
   1	5
   1	1
   1	0
   1	−1
   1	−5
   −1	5
   −1	1
   −1	0
   −1	−1
   −1	−5

   
   
   

2. What relationship do you see between the number of x-intercepts and the variables a and q in the quadratic function y = a(x − p)2 + q?

Save your responses in your course folder.

 

Share 2

 

Share your responses from Try This 2 with a partner or group.

 

Summarize your discussion by creating a rule that describes how to determine the number of x-intercepts in a quadratic function in the form y = a(x − p)2 + q.

 

Save your responses in your course folder.

 

Add your new rule that relates the variables a and q to the number of x-intercepts to the list of rules you started in Lesson 1, Share 1, question 4. You should now have five rules.