# OpenStax-CNX

You are here: Home » Content » Quadratic Homework -- Problems: Completing the Square

## Navigation

### 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.

# Quadratic Homework -- Problems: Completing the Square

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

Summary: Practice homework set on completing the square.

Note: You are viewing an old version of this document. The latest version is available here.

## Exercise 1

A pizza (a perfect circle) has a 3" radius for the real pizza part (the part with cheese). But they advertise it as having an area of 25 ππ size 12{π} {} square inches, because they include the crust. How wide is the crust?

## Exercise 2

According to NBA rules, a basketball court must be precisely 94 feet long and 50 feet wide. (That part is true—the rest I’m making up.) I want to build a court, and of course, bleachers around it. The bleachers will be the same depth (*by “depth” I mean the length from the court to the back of the bleachers) on all four sides. I want the total area of the room to be 8,000 square feet. How deep must the bleachers be?

## Exercise 3

Recall that the height of a ball thrown up into the air is given by the formula:

h ( t ) = h o + v o t 16 t 2 h ( t ) = h o + v o t 16 t 2 size 12{h $$t$$ =h rSub { size 8{o} } +v rSub { size 8{o} } t - "16"t rSup { size 8{2} } } {}

I am standing on the roof of my house, 20 feet up in the air. I throw a ball up with an initial velocity of 64 feet/sec. You are standing on the ground below me, with your hands 4 feet above the ground. The ball travels up, then falls down, and then you catch it. How long did it spend in the air?

Solve by completing the square.

## Exercise 4

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

## Exercise 5

x 2 10 x + 3 = 5 x 2 10 x + 3 = 5 size 12{x rSup { size 8{2} } - "10"x+3=5} {}

## Exercise 6

x 2 + 8x + 20 = 0 x 2 + 8x + 20 = 0 size 12{x rSup { size 8{2} } +8x+"20"=0} {}

## Exercise 7

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

## Exercise 8

3x 2 18 x + 12 = 0 3x 2 18 x + 12 = 0 size 12{3x rSup { size 8{2} } - "18"x+"12"=0} {}

## Exercise 9

Consider the equation x2+4x+4=cx2+4x+4=c size 12{x rSup { size 8{2} } +4x+4=c} {} where cc size 12{c} {} is some constant. For what values of cc size 12{c} {} will this equation have…

• a. Two real answers?
• b. One real answer?
• c. No real answers?

## Exercise 10

Solve by completing the square: x2+6x+a=0x2+6x+a=0 size 12{x rSup { size 8{2} } +6x+a=0} {}. (aa size 12{a} {} is a constant.)

## Content actions

### Add 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