# Connexions

You are here: Home » Content » Advanced Algebra II: Activities and Homework » Introduction to Quadratic Equations

### Lenses

What is a lens?

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

#### Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
• Featured Content

This collection is included inLens: Connexions Featured Content
By: Connexions

"This is the "main" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing about them in […]"

Click the "Featured Content" link to see all content affiliated with them.

Click the tag icon to display tags associated with this content.

#### Also in these lenses

• Busbee's Math Materials

This collection is included inLens: Busbee's Math Materials Lens
By: Kenneth Leroy Busbee

Click the "Busbee's Math Materials" link to see all content selected in this lens.

Click the tag icon to display tags associated with this content.

### Recently Viewed

This feature requires Javascript to be enabled.

### Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Inside Collection:

Collection by: Kenny M. Felder. E-mail the author

Module by: Kenny M. Felder. E-mail the author

Summary: An introduction to quadratic equations.

For exercises #1-5, I have two numbers x x size 12{x} {} and y y size 12{y} {} . Tell me everything you can about x x size 12{x} {} and y y size 12{y} {} if…

## Exercise 1

x + y = 0 x + y = 0 size 12{x+y=0} {}

## Exercise 2

xy = 0 xy = 0 size 12{ ital "xy"=0} {}

## Exercise 3

xy = 1 xy = 1 size 12{ ital "xy"=1} {}

## Exercise 4

xy > 0 xy > 0 size 12{ ital "xy">0} {}

## Exercise 5

xy < 0 xy < 0 size 12{ ital "xy"<0} {}

## Exercise 6

OK, here’s a different sort of problem. A swimming pool is going to be built, 3 yards long by 5 yards wide. Right outside the swimming pool will be a tiled area, which will be the same width all around. The total area of the swimming pool plus tiled area must be 35 yards.

• a. Draw the situation. This doesn’t have to be a fancy drawing, just a little sketch that shows the 3, the 5, and the unknown width of the tiled area.
• b. Write an algebra equation that gives the unknown width of the tiled area.
• c. Solve that equation to find the width.
• d. Check your answer—does the whole area come to 35 yards?

Solve for x x size 12{x} {} by factoring.

## Exercise 7

x 2 + 5x + 6 = 0 x 2 + 5x + 6 = 0 size 12{x rSup { size 8{2} } +5x+6=0} {}

Check your answers by plugging them into the original equation. Do they both work?

## Exercise 8

2x 2 16 x + 15 = 0 2x 2 16 x + 15 = 0 size 12{2x rSup { size 8{2} } - "16"x+"15"=0} {}

## Exercise 9

x 3 + 4x 2 21 x = 0 x 3 + 4x 2 21 x = 0 size 12{x rSup { size 8{3} } +4x rSup { size 8{2} } - "21"x=0} {}

## Exercise 10

3x 2 27 = 0 3x 2 27 = 0 size 12{3x rSup { size 8{2} } - "27"=0} {}

Solve for x x size 12{x} {} . You may be able to do all these without factoring. Each problem is based on the previous problem in some way.

## Exercise 11

x 2 = 9 x 2 = 9 size 12{x rSup { size 8{2} } =9} {}

## Exercise 12

( x 4 ) 2 = 9 ( x 4 ) 2 = 9 size 12{ $$x - 4$$ rSup { size 8{2} } =9} {}

## Exercise 13

x 2 8x + 16 = 9 x 2 8x + 16 = 9 size 12{x rSup { size 8{2} } - 8x+"16"=9} {}

## Exercise 14

x 2 8x = 7 x 2 8x = 7 size 12{x rSup { size 8{2} } - 8x= - 7} {}

## Content actions

PDF | EPUB (?)

### What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

PDF | EPUB (?)

### What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

#### Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

#### Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks