Lesson 4

Lesson 4: The Quadratic Formula

 

Focus

 

In the design industry, after a new product has been envisioned, a prototype is often built to test the concept. Once the design is established, it is easy to create variety in the product. In the case of a car, a manufacturer may produce five different colours, offer an automatic or standard transmission, and provide the choice of a standard or deluxe interior. Regardless of which combination of features is selected by the customer, the manufacturer can roll out the desired vehicle because the design has been standardized.

 

In this lesson you will use a formula to solve quadratic equations. Like the designer of a prototype, you will derive the formula by working with a “prototype,” or a specific example. You will discover that you can apply the formula or design to any quadratic equation in order to determine its roots.

 

Outcomes

 

At the end of this lesson you will be able to

• derive the quadratic formula using deductive reasoning

• solve a quadratic equation of the form ax2 + bx + c = 0 by applying the quadratic formula

• explain, using examples, how the discriminant may be used to determine whether a quadratic equation has two, one, or no real roots; and relate the number of zeros to the graph of the corresponding quadratic function

• select a method for solving a quadratic equation, justify the choice, and verify the solution

Lesson Questions

 

You will investigate the following questions:

• How is the quadratic formula related to the strategy of completing the square?
  
  
• How does a mathematical formula reveal the nature of the solutions to a problem?

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 4 Glossary Terms and Formula Sheet
  
  
• work under Project Connection