Math 30-1

Chapter 3 Polynomial Functions

Lesson 3.4  Equations and Graphs of Polynomial Functions

Support Documents

Answer pages

You should be checking your work for EVERY question you do!

To make that easy, you can download THIS DOCUMENT which has the answers for all the practice problems in the text.

You can print it, though it would be a lot of pages.

I think the best choice would be to keep the file handy, and have it open on your computer, ready to check answers every time you are doing practice problems.

This saves you the time of flipping to the back of the book every time you need to check an answer.

Solution Pages

These documents provide MORE than just answers, they provide more detailed solutions to all the questions in your textbook.

I strongly encourage you to download these, and keep them handy as you do your work

You can print these files, though it would be a lot of pages.

I think the best choice would be to keep these files handy, and have the current file for the unit you are working on,  open on your computer, ready to check answers every time you are doing practice problems.

Solutions LINK

Formula Page

Math 30-1 is an academic course and you will be expected to memorize a lot of what you are covering in class.

Since this is a diploma exam course, there is a STANDARD formula page that you should be using whenever you are working on math.

You will want to get used to what is there so you will know exactly what to expect when you write your diploma exam.

For this reason you should also NOT write anything on this page,  since those extra notes won’t be there when you write your diploma exam!

Formula Page LINK

Focus on...

Lesson Objectives

•	describing the relationship between zeros, roots, and x-intercepts of polynomial functions and equations

•	sketching the graph of a polynomial function without technology

•	modelling and solving problems involving polynomial functions

Focus on...  Activity

The FOCUS section introduces the main concept that will be covered in the lesson.

TEXT Page 136

Read/Work through the  Focus  section at the top of page 136 in  your textbook.

Do your best to answer the questions given in this section.

These ideas will all be covered in the lesson.

Video Tutorial  (Focus)

Investigate   Sketching the Graph of a Polynomial Function

The investigation provides the background for the ideas presented in the lesson.

TEXT Pages 136 - 137

Read/Work through the  Investigate  section on Pages 136 - 137 in your textbook.

If you are working on your own,  answer the questions, AS BEST YOU CAN, before you view the Video Tutorials that follow.

Once you have done that,  view the videos for help with this section.

Here is the Desmos page I used in my video tutorial

Part A:	The Relationship Among the Roots, x-Intercepts, and Zeros of a Function

Video Tutorial Question 1   (INV 1)

Video Tutorial Question 2     (INV 2)

Reflect and Respond

Question 3
I answered this when I did Question 2

Part B:	Determine When a Function Is Positive and When It Is Negative

Video Tutorial Question 4    (INV 4)

Reflect and Respond

Question 5

The sign of f(x)  changes when it crosses the x - axis.
When there are two identical zeroes,  the sign of f(x)  does NOT change.

Part C:	Sketch the Graph of a Polynomial Function

Video Tutorial Questions 6 - 7   (INV 67)

Reflect and Respond

Question 8 Do your best to describe this in your own words.
The rest of the lesson will have numerous examples to work on to practice these ideas.

Link the Ideas

Link the Ideas summarizes the math in the lesson.
A presentation of ideas connected to the lesson focus.

TEXT Page 138

Read/Work through the  Link the Ideas  section on Page 138 in your textbook.

Watch

Video Tutorial   (LINK)

Examples

Examples will give you TOOLS for solving problems, and also show you that there may be different ways to approach a question.

Example 1  Analyse Graphs of Polynomial Functions

TEXT Pages 138 - 139

Work through Example 1 on Pages 138 - 139 in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 2  Analyse Equations to Sketch Graphs of Polynomial Functions

TEXT Pages 140 - 142

Work through Example 2 on Pages 140 - 142 in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 3  Apply Transformations to Sketch a Graph

TEXT Pages 143 - 144

Work through Example 3 on Pages 143 - 144 in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

OPTIONAL!
I had an idea about how to illustrate the process we went through in this example.
I wanted to transform EVERY point on the original graph and see how that ended up on the new graph.
I think it turned out really well, use the links below if you want to check it out!

Video Tutorial

Desmos Page I used in the video

Example 4  Model and Solve Problems Involving Polynomial Functions

TEXT Pages 145 - 146

Work through Example 4 on Pages 145 - 146 in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Key Ideas

Key Ideas summarizes the main new concepts of the lesson.

•	Carefully read through each of the bullet points in this section.

•	If you are unclear about any of these ideas,  ASK YOUR TEACHER FOR HELP!

Check Your Understanding    (Practice Problems)

Doing Practice Problems

Practice problems reinforce the math presented in this lesson.

•	Work through the practice problems for this lesson.
	These problems are for practice, you don’t need to hand them in!
	(your teacher may assign specific questions for you to complete)

•	Use the answers in the back of the book to CHECK YOUR WORK!

•	If you make a mistake, TRY TO FIX IT!

•	If you need help or want more information, view the video solutions provided.

•	If you still need more help,  CONTACT YOUR TEACHER!

NOTE!
There are MANY practice questions.
In the interests of time,  I will be selectively skipping some of them.
You have access to the solutions, and you can use those for help as needed.
If the presentation seems straight-forward, I won’t create a video.
I’m hoping that as this course continues to be developed, that if MORE HELP is needed for a specific question,  the missing videos can be added at a later date.

Types of Practice Problems

Practice 
These questions allow you to check your understanding of the concepts. 
You can often do the first few questions by checking the Link the Ideas notes or by following one of the worked Examples.

Apply 
These questions ask you to apply what you have learned to solve problems. 
You can choose your own methods of solving a variety of problem types.

Extend 
These questions may be more challenging. 
Many connect to other concepts or lessons. 
They also allow you to choose your own methods of solving a variety of problem types.

Create Connections
These questions focus your thinking on the Key Ideas and also encourage communication. 
Many of these questions also connect to other subject areas or other topics within mathematics.

Mini Lab
These questions provide hands-on activities that encourage you to further explore the concept you are learning.

Notes

Question 1,    I didn’t do a video for this one.

Question 2,    I didn’t do a video for this one.

Question 8,    I didn’t do a video for this one.

Question 15,    I didn’t do a video for this one.

Question 18,    I didn’t do a video for this one.

Question 19,    I didn’t do a video for this one.

Question 23,    I didn’t do a video for this one.

Video Solution Links

Check your work for every problem you do!
If you make a mistake,  try to fix it!
Use the video solutions for more information.
If a problem still doesn’t make sense, ASK YOUR TEACHER FOR HELP!

({{ ,  , "Question 3", "Question 4", "Question 5"}, {"Question 6", "Question 7",   , "Question 9", "Question 10"}, {"Question 11", "Question 12", "Question 13", "Question 14",  }, {"Question 16", "Question 17",  ,  , "Question 20"}, {"Question 21", "Question 22",  , , }})

I didn’t create videos for any of the CC questions.
These are all GREAT questions,  and the mini-lab would be especially worthwhile, but it’s a major task to complete that one.
You have the solutions to help you if you need to tackle any of these.