Math 20-2

Chapter 6 Quadratic Functions

Lesson 6.4   Vertex Form of a Quadratic Function

GOAL

The goal of this lesson is stated at the top of page 354 in your textbook, and is also written below.
Keep this in mind as you work through the lesson material.

Graph a quadratic function in the form y = ((a(x-h))^2)+k, and relate the characteristics of the graph to its equation.

Explore...

Try to answer the question in the sidebar on page 354.

Because this is an exploration,  I would recommend using Desmos to do this quickly and easily.

I don’t want to give you an easy way out, but... if it means the difference between actually doing this or skipping it.... THIS LINK is to a Desmos page with all the graphs from the exploration.

Video Introduction

Investigate the Math

Investigate an idea or problem, with a partner if possible.
The investigation provides the background for the ideas presented in the lesson.

TEXT Pages 354 - 355

Read/Work through the Investigate section on Pages 354-355 in your textbook.

Go through this material,  AS BEST YOU CAN,  before you view the video tutorials that follow.
NOTE!   This is an investigation,  if you want to explore these ideas, you will need to do that before you watch the videos,  since I will be giving “answers” right from the start.

For a quick introduction to this idea, view THIS VIDEO  (about 20 seconds)

Introduction

Video Tutorial  (INV0)

?  How could Judy predict what the graph of the quadratic function would look like?

Be sure to work through the investigation as best as you can, before you watch the video!!

Part A  Video Tutorial  (INV A)

Part B  Video Tutorial      (INV B)

Part C  Video Tutorial      (INV C)

Part D  Video Tutorial        (INV D)

Part E  Video Tutorial       (INV E)

Vertex Form interpretation  (VertexForm)

Reflecting

Video Tutorial  (INV G)

Part H  Yes. this is true.

Part I  Video Tutorial

Part J, this is subjective, but the vertex form is very useful,  if you want to find the vertex!
But it’s not as useful for finding intercepts.
This is the reason for writing the function equation in different forms for different purposes.

Apply the Math  (Examples)

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

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

Example 1  Sketching the graph of a quadratic function given in vertex form

TEXT Page 356

Work through Example 1 on Page 356 in your textbook.

Watch

Video Tutorial

Your Turn

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  Determining the equation of a parabola using its graph

TEXT Pages 357 - 358

Work through Example 2 on Pages 357 - 358 in your textbook.

The video below is a time lapse showing the shadows cast by a block of wood over time.
You would have to measure really accurately to see the difference in shadow lengths, but it does illustrate the ideas of this example.

Shadows, time lapse

Watch

Video Tutorial

Your Turn

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  Reasoning about the number of zeros that a quadratic function will have

TEXT Pages 358 - 359

Work through Example 3 on Pages 358 - 359 in your textbook.

HERE is the page I used to make the video for this question.

Watch

Video Tutorial

Your Turn

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  Solving a problem that can be modelled by a quadratic function

TEXT Pages 359 - 361

Work through Example 4 on Pages 359 - 361 in your textbook.

Watch

Video Tutorial

Your Turn

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

In Summary

Key Ideas and Need to Know 
Presents and 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!

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!

Types of Practice Problems

Check Your Understanding questions require basic understanding of the ideas of the  lesson.

Practising questions will require you to dig deeper for a solution.

Closing  A summary question that often asks YOU to explain ideas in your own words.

Extending questions offer enrichment and extension.

Notes

Question 6,    I didn’t do a video for this one.
This has been covered a lot in this lesson.
Check the answer in the back for some possible ideas.

Question 16,    I didn’t do a video for this one.
From the book...
e.g., Agree. 
It is easier to graph the quadratic function when it is in vertex form because you can determine the vertex, the y-intercept, and direction of the graph without doing any calculations.

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 9", "Question 10"}, {"Question 11", "Question 12", "Question 13", "Question 14", "Question 15"}, { , "Question 17", "Question 18", "Question 19", }})