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

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

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

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  1. 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?

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

  3. What is a quadratic? x2 + 3 = 5 2x2 – 4x = 19 -4x2 -9x +99 = 0

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

  5. Not verifying answers after solving.

  6. 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?

  7. square shaped wall .25 gallons per square foot length = width 4 gallons total area = w x l area = w2 .25*area = 4 .25*w2 = 4 w2 = 16

  8. VERFIY: what do my answers mean? do they make sense? .25*area = 4 .25*w2 = 4 w2 = 16 w = 4, w = -4

  9. In this lesson you have learned how to create and solve inequalities by using a quadratic relationship

  10. 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?

  11. w width is 2 inches longer 2 dollars per square inch l = w - 2 96 dollars total area = w * l area = w(w-2) 2*area = 96 2(w)(w-2) = 96 w2 – 2w - 48 = 0

  12. VERFIY: what do my answers mean? do they make sense? 2*area = 96 (w+6)(w-8)= 0 2(w)(w-2) = 96 w= -6, w= 8 w2 – 2w - 48 = 0

  13. Explore how changing the amount per square inch/foot (for both problems!) changes the amount of area allowed • Explore different relationships between length and width of cakes (will there always be a quadratic?) • 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?

  14. 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?

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