Lesson 1: Sketching Polynomial Functions

 

Focus

 

The spaces, shapes, and forms of graphic design rely on many principles of mathematics. M.C. Escher, one of the world’s most famous graphic artists, is noted for the complex mathematical aspects of his work. Today, graphic design is a competitive industry that is dependant on computers and design software. Designers are expected to grasp fundamental math principles and concepts to solve design problems.

A graphic artist may want to capture the contour of an abstract design. A curve following the graph of a polynomial function may be useful in the design. A polynomial function that could be used to describe this curve is f(x) = 23x4 − 69x3 − 2208x2 + 8924x + 11 040. This same function can be written in an equivalent factored form, f(x) = 23(x + 10)(x + 1)(x − 6)(x − 8). Both forms express the same polynomial, but each form will allow you to more easily obtain different information.

 

In this lesson you will learn how the factored form and the expanded form of a function can help identify different behaviours and characteristics about the corresponding graph.

 

Lesson Outcomes

 

At the end of this lesson you will be able to sketch the graph of a polynomial function given the equivalent expanded and factored forms, without the use of technology.

 

Lesson Questions

 

You will investigate the following questions:

• How does the expanded form of a polynomial function help identify the end behaviour of the corresponding graph?
  
• How does the factored form of a polynomial function help identify the x-intercepts of the corresponding graph?

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 Glossary Terms
• 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.

 

Remember that the questions and activities you will encounter provide you with the practice and feedback you need to successfully complete this course. You should complete all questions and place your responses in your course folder. Your teacher may wish to view your work to check on your progress and to see if you need help.

 

Time

 

Each lesson in Mathematics 30-1 Learn EveryWare is designed to be completed in approximately two hours. You may find that you require more or less time to complete individual lessons. It is important that you progress at your own pace, based on your individual learning requirements.

 

This time estimation does not include time required to complete Going Beyond activities or the Module Project.