how do you find out how much area a bucket of paint will cover? for example
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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. What is a quadratic?. x 2 + 3 = 5 - PowerPoint PPT PresentationTRANSCRIPT
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 Lessonsquare shaped wall
length = widtharea = 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 Practicewidth is 2 inches longer
l = w - 2area = 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 Quiz1. 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?