How do you find out how much area a bucket of paint will cover?

For examplehow big a wall can a 4 gallon can of

paint cover?

In this lesson you will learn how to create and solve

equationsby modeling a situation with a

quadratic relationship

Let’s Review

What is a quadratic?

x2 + 3 = 52x2 – 4x = 19-4x2 -9x +99 = 0

Let’s Review

Keep in mind that quadratics can be solved in many ways:-Factoring-Taking roots-Using the quadratic formula-Completing the square-Graphing

A Common Mistake

Not verifying answers after solving.

Core Lesson

We will investigate the following problem:You have a 4 gallon bucket of pink paint to

paint your room; it takes .25 gallons to cover 1 square foot of wall. If you have a square shaped wall, what width/height walls will

your paint bucket cover?

Core Lesson

square shaped wall

length = width

area = w x larea = w2

.25 gallons per square foot

.25*area

4 gallons total

= 4 .25*w2 = 4 w2 = 16

Core Lesson

.25*area = 4 .25*w2 = 4 w2 = 16 w = 4, w = -4

VERFIY: what do my answers mean? do they make sense?

In this lesson you have learned how to create and solve

inequalitiesby using a quadratic

relationship

Guided Practice

A cake maker can earn 2 dollars for every square inch of cake that he bakes. If the cake maker bakes cakes that are always 2 inches wider than they are long, for what widths of cake will the cake maker earn 96 dollars?

Guided Practice

width is 2 inches longer

l = w - 2

area = w * larea = w(w-2)

2 dollars per square inch

2*area

96 dollars total

= 962(w)(w-2) = 96

w2 – 2w - 48 = 0

w

Guided Practice

VERFIY: what do my answers mean? do they make sense?

2*area = 962(w)(w-2) = 96

w2 – 2w - 48 = 0

(w+6)(w-8)= 0 w= -6, w= 8

Extension Activities

a. Explore how changing the amount per square inch/foot (for both problems!) changes the amount of area allowed

b. Explore different relationships between length and width of cakes (will there always be a quadratic?)

c. Use the computer to explore “Metcalf’s Law”, which describes the value of telecommunications companies based on their users – how it is related to our work here?

Quick Quiz

1. A homebuilder charges $100 per square foot of home. A family wants to spend $50,000 building a home; their home will have a width 1.5 times more than its length. What length of house will they build?

2. Jennie wants to build a garden in her backyard for $50. If she builds a square garden that costs 2 dollars per square foot, what is the size of the the sides of her garden?