Math 20-1

Chapter 3 Quadratic Functions

Lesson 3.1   Investigating Quadratic Functions in Vertex Form

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

•	identifying quadratic functions in vertex form

•	determining the effect of a, p, and q  on the graph of y = ((a(x-p))^2)+q

•	analysing and graphing quadratic functions using transformations

Focus on...  Activity

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

TEXT Page 142

Read/Work through the  Focus  section at the top of page 142 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

Link to the Desmos file I used in the video

Investigate  Graphs of Quadratic Functions in Vertex Form

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

You are welcome to do this investigation using grid paper, but I strongly recommend using technology, specifically the online graphing program DESMOS.
It’s easy to use, and because it’s easy, will hopefully encourage  you to “dig deeper” as you explore the ideas of this lesson.

TEXT Pages 143 - 144

Read/Work through the  Investigate  section on Pages 143 - 144 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!

You may not have other students to work with.  
No worries!  
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:	Compare the graphs of f(x) = (x^2)  and f(x) = a (x^2),  a ≠ 0

This Desmos page is a good staring place for this investigation.

Video Tutorial Questions 1 - 2  INV A

Reflect and Respond

Video Tutorial Question 3
This is supposed to be an investigation, so it’s best for you to describe your findings in YOUR OWN WORDS!
Then check your findings by testing them with some sample functions to see if they match your description.

Part B:	Compare the graphs of f(x) = (x^2)  and f(x) = (x^2)+q

Video Tutorial Questions 4 - 6   INV B

Video Tutorial Question 6
This is supposed to be an investigation, so it’s best for you to describe your findings in YOUR OWN WORDS!
Then check your findings by testing them with some sample functions to see if they match your description.

Part C:	Compare the graphs of f(x) = (x^2)  and f(x) = (((x-p))^2)

Video Tutorial Questions 7 - 9  INV C

Video Tutorial Question 9
This is supposed to be an investigation, so it’s best for you to describe your findings in YOUR OWN WORDS!
Then check your findings by testing them with some sample functions to see if they match your description.

Link the Ideas

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

These ideas are best explored visually.
I strongly encourage you to watch the video but to ALSO work with the online graphs you can link to.
The ideas of this lesson are a building block for this course AND the next course in the sequence  (Math 30-1)

TEXT Pages 144 - 147

Read/Work through the  Link the Ideas  section on Pages 144 - 147 in your textbook.

A DESMOS page you can use to reinforce visually, all the information given in this section

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  Sketch Graphs of Quadratic Functions in Vertex Form

TEXT Pages 148 - 150

Work through Example 1 on Pages 148 - 150 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  Determine a Quadratic Function in Vertex Form Given Its Graph

TEXT Pages 151 - 153

Work through Example 2 on Pages 151 - 153 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 number of x-Intercepts using a and q

TEXT Pages 153 - 154

Work through Example 3 on Pages 153 - 154 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  Model Problems Using Quadratic Functions in Vertex Form

TEXT Pages 154 - 156

Work through Example 4 on Pages 154 - 156 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 5,    I didn’t do a video for this one.
A great question to use technology on.
Hypothesis (equation of function)  ⟶  graph  (check your hypothesis)

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.
EVERY quadratic function has ONE y-intercept.

Question 15,    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 20,    I didn’t do a video for this one.

Question 22,    Below is the Desmos page I used to illustrate my quadratic model
LINK

Below is a link to a Geogebra applet that models an actual time lapse video of a basketball shot.
You can control the parameters to find the equation that models the shot.

Geogebra Applet

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 6", "Question 7", "Question 8", "Question 9"}, { ,  , "Question 13", "Question 14"}, { , "Question 17",  , "Question 19"}, {"Question 21", "Question 22", "Question 23", }})

I didn’t make a video for any of the CC questions.
For CC 26,  check out the link below for an amazing example of “parabola art” (as well as many other functions)
You can click on the animation controls for “action”

LINK