Lesson 3

Lesson 3: Completing the Square

Focus

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Riding a snowmobile is a great winter activity. Running your snowmobile up a slope, jumping the sled into the air, and landing in soft snow can be exhilarating.

Competitions are sometimes held to see who can jump the farthest or the highest. The path of the snowmobile can be modelled and predicted using quadratic functions. What is learned from these functions can guide riders to greater length or height in a jump.

Up to this point in the module you have only worked with the quadratic function in vertex form, y = a(x − p)2 + q. This form is excellent for modelling situations in which there is a maximum or minimum value. This form enables you to know what the maximum height of a jump might be by looking at the coordinates of the vertex, which can be read directly from the p- and q-values of the function.

In this lesson you will encounter the standard form of the quadratic function.The standard form is written as f(x) = ax2 + bx + c or y = ax2 + bx + c.

The standard form of the quadratic function is more useful in predicting distance of jumps and modelling some other real-life situations. You will learn to model situations in the standard form and convert the standard form to the vertex form.

Outcomes

At the end of this lesson you will be able to

• write the quadratic function given in the standard form, y = ax2 + bx + c, in the vertex form, y = a(x − p)2 + q, by completing the square
  
  
• explain the reasoning for the process of completing the square as shown in a given example
  
  
• identify, explain, and correct errors in an example of completing the square

Lesson Questions

You will investigate the following question:

• How do you complete the square to convert a quadratic function in the standard form, y = ax2 + bx + c, into the vertex form, y = a(x − p)2 + q?

Assessment

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

• completion of the Lesson 3 Assignment (Download the Lesson 3 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