Lesson 1

Self-Check 1

In Share 1, you created a table to organize your observed patterns and the three general rules you developed to describe the effect of a, p, and q on y = a(x − p)2 + q. Use your table and the graphs provided below to help answer the following questions.

1. Match each equation with its graph.
   
   
   1. y = x2 Answer
      
      
   2. y = 3x2 Answer
      
      
   3. y = −4x2 Answer
      
      
   4. y = 0.3x2 Answer
      
      
   5. y = x2 + 5 Answer
      
      
   6. y = x2 − 4 Answer
      
      
   7. y = (x − 4)2 Answer
      
      
   8. y = (x + 5)2 Answer
      
      
2. Which of the graphs has a maximum value? What is that value? Answer
   
   
3. What is the minimum value of graph 2? Answer
   
   
4. What is the domain and range of graph 7? Answer
   
   
5. Why are all of the functions in Try This 1 considered to be quadratic functions? Answer
   
   
6. Look at the equations in the chart. Without graphing, predict what each graph would look like.
   
   
    

   Equation y = a(x − p)2 + q	What Does a Tell You About This Graph?	What Does p Tell You About This Graph?	What Does q Tell You About This Graph?
   y = 6(x − 3)2 + 5
   y = 6(x − 3)2 − 4
   y = 6x2 + 1
   y = −6(x + 3)2 + 1
   y = −0.5(x − 3)2 + 1

   
   
   Answer