Math 20-1

Chapter 4  Quadratic Equations

Lesson 4.1   Graphical Solutions of Quadratic Equations

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

•	describing the relationships between the roots of a quadratic equation, 
	the zeros of the corresponding quadratic function, 
	and the x-intercepts of the graph of the quadratic function

•	solving quadratic equations by graphing the corresponding quadratic function

Focus on...  Activity

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

There isn’t a Focus section for this lesson.

TEXT Page 206

Read/Work through the  Focus  section at the top of page 206 in  your textbook.

Do your best to answer the questions given in this section.
These ideas will all be covered in the lesson.

If you would like to experiment a bit before you get into the lesson, check out the link below.

Desmos page (water jet simulation)

Investigate  Solving Quadratic Equations by Graphing

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

TEXT Pages 206 - 207

Read/Work through the  Investigate  section on Pages 206 - 207 in your textbook.

I would recommend doing the investigation using Desmos to help with the graphing.

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 videos for help with this section.

Investigate

Video Tutorial Question 1   (INV 1)

Video Tutorial Question 2     (INV 2)

Reflect and Respond

Video Tutorial Question 3     (INV 3)

Question 3, some notes...

a) You could aim the jet at a sharper angle to make the stream land closer to the jet or at a more gentle angle to make it land farther away.

b) Yes. If two streams were aimed at different angles, the two would travel up to different heights, but could both land at the same spot.

Link the Ideas

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

TEXT Page 208

Read/Work through the  Link the Ideas  section on Page 208 in your textbook.

Watch

Video Tutorial  LINK A  (vocabulary)

Video Tutorial  LINK B  (graphing to solve)

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  Quadratic Equations With One Real Root

TEXT Pages 208 - 209

Work through Example 1 on Pages 208 - 209 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  Quadratic Equations With Two Distinct Real Roots

TEXT Pages 210 - 212

Work through Example 2 on Pages 210 - 212 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  Quadratic Equations With No Real Roots

TEXT Page 212

Work through Example 3 on Page 212 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.

I didn’t do a video here... rearrange the equation and graph, and you can see it DOESN’T cross the x-axis, so there are no solutions.

Example 4  Solve a Problem Involving Quadratic Equations

TEXT Page 213

Work through Example 4 on Page 213 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.

Not really anything to do here,  change the equation, and graph, just like in Example 4.
Below, a Desmos screenshot.

The towers are   169.3 - 30.7 = 138.6m apart

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 9,    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 create a video,  but THIS DESMOS page has the plots of the quadratic functions to help in interpreting the question

Question 13,    Here is the Desmos page I used to create the video

Question 14,    I didn’t do a video for this one.  (check the solution for help)
A good question would be,  HOW did they arrive at the equation for the height?

Question 15,    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 10"}, { ,  , "Question 13",  ,  }})

I didn’t create a video for any of the CC questions. 
Check the solution document for help with these.