How do you find out how much area a bucket of paint will cover? For example how big a wall can a 4 gallon can of paint cover?

In this lesson you will learn how to create and solve equations by modeling a situation with a quadratic relationship

Let’s Review What is a quadratic? x = 5 2x 2 – 4x = 19 -4x 2 -9x +99 = 0

Let’s Review Keep in mind that quadratics can be solved in many ways: -F-Factoring -T-Taking roots -U-Using the quadratic formula -C-Completing the square -G-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?

square shaped wall length = width area = w x l area = w 2.25 gallons per square foot.25*area 4 gallons total = 4.25*w 2 = 4 w 2 = 16

Core Lesson.25*area= 4.25*w 2 = 4 w 2 = 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 inequalities by 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?

width is 2 inches longer l = w - 2 area = w * l area = w(w-2) 2 dollars per square inch 2*area 96 dollars total = 96 2(w)(w-2) = 96 w 2 – 2w - 48 = 0 w

VERFIY: what do my answers mean? do they make sense? 2*area= 96 2(w)(w-2) = 96 w 2 – 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?