Math 20-2

Chapter 6 Quadratic Functions

Lesson 6.3   Factored Form of a Quadratic Function

GOAL

The goal of this lesson is stated at the top of page 337 in your textbook, and is also written below.
Keep this in mind as you work through the lesson material.

Relate the factors of a quadratic function to the characteristics of its graph.

Explore...

Try to answer the question in the sidebar on page 337.

Watch

Video Tutorial

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 Page 337

Read/Work through the Investigate section on Page 337 in your textbook.

Go through this material,  AS BEST YOU CAN,  before you view the video tutorials that follow.

Demonstration

This is not the exact problem being worked on, but it will give you some ideas about the concept being investigated.

?  What dimensions should Ataneq use to maximize the area of the kennel?

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

Video Tutorial

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  Graphing a quadratic function given in standard form

TEXT Pages 338 - 339

Work through Example 1 on Pages 338 - 339 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  Using a partial factoring strategy to sketch the graph of a quadratic function

TEXT Pages 339 - 341

Work through Example 2 on Pages 339 - 341 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 3  Determining the equation of a quadratic function, given its graph

TEXT Pages 341 - 342

Work through Example 3 on Pages 341 - 342 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 4  Solving a problem modelled by a quadratic function in factored form

TEXT Pages 343 - 344

Work through Example 4 on Pages 343 - 344 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

Practice Problem 17 Demonstration  (Optional)

Practice Problem 17 illustrates a common question about projectile motion and the resulting parabola.
This is optional but hopefully helpful for understanding.

The Question
A water rocket was launched from the ground, with an initial velocity of 32 m/s.
The rocket achieved a height of 44 m after 2 s of flight.
The rocket was in the air for 6 s.
a)	Determine the quadratic function that models the height of the rocket over time.
b)	State the domain and range of the function.

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 5,    I didn’t do a video for this one.
I answered this when I did question 4.

Question 15,    I didn’t do a video for this one.
A great idea for a question, but... the assumption here would be that the pelican hits the water,  slows down till the point where it catches a fish, then accelerates back up out of the water, gaining speed and exiting the water at the same speed it entered it.   I know that math questions can often be a “stretch”, but this is a bit much...

Question 14,    I didn’t do a video for this one.
A quadratic function can have 2 zeros, 1 zero, or no zeros.
Those are the only possibilities.
You can experiment and graph different quadratics to see this for yourself.

Question 17,    be sure to check out the demonstration that was in the lesson, I think it will help with understanding this question.
Also note, not that it makes any difference to the answer, but the text has an error,  the initial velocity of the water rocket would need to be 33 m/s to fit the other info given in the question.

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 10"}, {"Question 11", "Question 12", "Question 13",  ,  }, {"Question 16", "Question 17", "Question 18", "Question 19", "Question 20"}, {"Question 21", , , , }})