Lesson 1

Lesson 1: Investigating Quadratic Functions

 

Focus

 

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In this lesson you will learn about the vertex form of the quadratic function, y = a(x − p)2 + q. You will notice patterns between the values of a, p, and q in the function and the shape and position of the graph. You will then be able to predict and graph the path of a quad in a jump, a thrown football, a flying hockey puck, or any real-world projectile example.

 

Outcomes

 

At the end of this lesson you will be able to

• explain why y = a(x − p)2 + q is a quadratic function
  
  
• compare the graph of y = ax2 to the graph of y = x2, and state rules about the effect of a
  
  
• compare the graph of y = x2 + q to the graph of y = x2, and state a rule about the effect of q
  
  
• compare the graph y = a(x − p)2 to the graph of y = x2, and state a rule about the effect of p

Lesson Questions

 

You will investigate the following questions:

• How do the values of a, p, and q affect the appearance and placement of the graph of the function y = a(x − p)2 + q?
  
  
• What are the characteristics of quadratic functions and their graphs?

Assessment

Your assessment may be based on a combination of the following tasks:

• completion of the Lesson 1 Assignment (Download the Lesson 1 Assignment and save it in your course folder now.)
  
  
• course folder submissions from Try This and Share activities
  
  
• additions to Module 3 Glossary Terms and Formula Sheet
  
  
• work under Project Connection

Self-Check activities are for your own use. You can compare your answers to suggested answers to see if you are on track. If you are having difficulty with concepts or calculations, contact your teacher.

Materials and Equipment

 

You will need a graphing calculator and graph paper.