Math 20-1

Chapter 3 Quadratic Functions

Lesson 3.3   Completing the Square

Support Documents

Answer pages

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

To make that easy, you can download the solutions files which have 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 files handy, and have them open and ready every time you are working on math.

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

FOLDER LINK

Formula Page

Math 20-1 is an academic course and you will be expected to memorize a lot of what you are covering in class.

Your teacher will have expectations for the things you will see on a formula page.

The link below is to formula page that you can download and print to use with your course.

You may or may not be allowed to use this on tests, and you may or may not be allowed to ADD your own notes to these pages.

Use of this page depends on your teacher.

What goes on this page is also subjective, so it is subject to change!

Formula Page

Focus on...

Lesson Objectives

•	converting quadratic functions from standard to vertex form

•	analysing quadratic functions of the form y = a (x^2)+b x + c

•	writing quadratic functions to model situations

Focus on...  Activity

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

TEXT Page 180

Read/Work through the  Focus  section at the top of page 180 in  your textbook.

Do your best to answer the questions given in this section.
(pretty hypothetical at this point!)
These ideas will all be covered in the lesson.

Investigate  Completing the Square

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

This idea is HUGELY IMPORTANT!
I’ve taken time to work through each question of the investigation, one step at a time, to hopefully provide the support needed to GET THIS!
Take your time,  and do your best to GET THIS!
We will be using this method in this lesson as well as the next unit on Quadratic Equations.
It’s a super important idea....

TEXT Pages 180 - 182

Read/Work through the  Investigate  section on Pages 180 - 182 in your textbook.

A list of materials  you need for the Investigation is given in the side bar.

Your work will be a lot more efficient if you PLAN for and GATHER these items BEFORE you start the Investigation!

I will be using the Desmos online graphing calculator to do the graphing parts of the investigation.

I will provide links to the pages I use so you can follow along if that is what you choose to do.

If you are working on your own,  answer the questions, AS BEST YOU CAN, before you view the Tutorial that follows.
Once you have done that,  view the video for help with this section.

Part A:	Comparing Different Forms of a Quadratic Function

Video Tutorial Questions 1 - 2   INV A

Video Tutorial Question 3    INV B

Video Tutorial Question 4      INV C

Video Tutorial Question 5      INV D

Video Tutorial Question 6     INV E

Not super useful, but HERE is the Desmos page with the graphs I used in the videos for Questions 1 - 6

Part B:	Completing the Square

You can use the virtual algebra tiles that you can link to below, to work on this part of the investigation.
I give some help with using them in the Video Tutorial for Question 7

Algebra Tiles  LINK (Google Docs)

Video Tutorial Question 7   INV F

Video Tutorial Question 8    INV G     
(answers  do this yourself FIRST!!!!!!!!         INV H)

Video Tutorial Question 9   INV J

Video Tutorial Question 10  INV K

Reflect and Respond

Video Tutorial Question 11    INV L

Video Tutorial Question 12     INV M

Here is a link to the page I used in the video,  you can download this and PRINT it for reference.
You might potentially be able to use this as an add-on formula page, but that will be up to your teacher.

Link the Ideas

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

TEXT Page 183

Read/Work through the  Link the Ideas  section on Page 183 in your textbook.

Completing the square, “helper page”

THIS page, that you can download and print, has a set of steps to guide you through the process of completing the square.
There are also several video examples you can link to (if you read the file on your computer)

CSQ page

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  Convert From Standard Form to Vertex Form

TEXT Pages 184 - 186

Work through Example 1 on Pages 184 - 186 in your textbook.

Watch

Using Algebra Tiles can be helpful,  but in the video I will focus on algebraic methods.
You can use the textbook presentation if you want more help with using tiles to complete the square.

Video Tutorial  Part A

Video Tutorial  Part B

Video Tutorial  Part C

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  Part A

Video Tutorial  Part B

Video Tutorial  Part C

Example 2  Convert to Vertex Form and Verify

TEXT Pages 187 - 188

Work through Example 2 on Pages 187 - 188 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  Determine the Vertex of a Quadratic Function by Completing the Square

TEXT Pages 188 - 189

Work through Example 3 on Pages 188 - 189 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 4  Write a Quadratic Model Function

TEXT Pages 190 - 192

Work through Example 4 on Pages 190 - 192 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)

Note!   I wish the textbook would have provided more guidance about HOW to do many of these questions!
The method of completing the square is the focus of this lesson and I feel it would be most helpful to do the questions using that method.
You need that practice!
If you use your calculator to graph and then find the vertex,  yes,  that is a useful skill, but after a few times, there is not much to it.
I truly hope you won’t do “every” problem that way!
Since I won’t be doing ALL the practice problems,  I will focus on doing problems that are unique, and I will use the algebraic method of completing the square as much as possible.

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

Question 9,    I didn’t do a video for this one.

Question 10,    I didn’t do a video for this one.

Question 11,    I didn’t do a video for this one.

Question 12,    I didn’t do a video for this one.

Question 16,    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 20,    I didn’t do a video for this one.

Question 21,    I didn’t do a video for this one.

Question 27,    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 1", "Question 2", "Question 3", "Question 4", "Question 5"}, { , "Question 7", "Question 8",  ,  }, { ,  , "Question 13", "Question 14", "Question 15"}, { , "Question 17",  ,  ,  }, { , "Question 22", "Question 23", "Question 24", "Question 25"}, {"Question 26",  , "Question 28", , }})

({{"CC 29", "CC 30", "CC 31"}})