Lesson 4

Lesson 4: Properties of y = ax2 + bx + c

 

Focus

 

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From your work on Module 3 Project: Spray Park, you know that when water is spayed in a single stream, the path the water follows is in the shape of a parabola. The size and shape of that parabola depend on the angle and speed of the water as it leaves the spray nozzle.

 

The path can be modelled with a quadratic function, expressed either in the standard form, y = ax2 + bx + c, or in the vertex form, y = a(x − p)2 + q. How can you use the constants in the standard form of a quadratic function to figure out the distance the water will go?

 

In this lesson you will learn how to determine the characteristics of a function, including the vertex, axis of symmetry, y-intercept, roots, and width of the parabola when given a quadratic function in the standard form, y = ax2 + bx + c.

 

Outcomes

 

At the end of this lesson you will be able to

• describe the characteristics of a function expressed in the form y = ax2 + bx + c and explain the strategy used to arrive at those characteristics
  
  
• sketch the graph of a function given in the form y = ax2 + bx + c
  
  
• verify that a function given in the form y = ax2 + bx + c represents the same function as one given in the form y = a(x − p)2 + q

Lesson Questions

 

You will investigate the following questions:

• How do you determine the characteristics of a quadratic function in the form y = ax2 + bx + c?
  
  
• How can you determine whether two functions written in the forms y = ax2 + bx + c and y = a(x − p)2 + q represent the same function?

Assessment

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

• completion of the Lesson 4 Assignment (Download the Lesson 4 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

Materials and Equipment

 

You will need graph paper.