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Published byGeraldine Wilkerson Modified over 9 years ago
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Let’s start with a problem today…Using only algebra, find
a cubic function with the given zeros. Answer should be in standard form. Support by graphing your answer…labeling your graph well!
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Modeling with Higher-Order Polynomials
Sec. 2.3b… Homework: p odd, 63, 67
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Practice Problems Dixie Packaging Company has contracted to make boxes with a volume of approximately 484 cubic inches. Squares are to be cut from the corners of a 20-in. by 25-in. piece of cardboard, and the flaps folded up to make an open box. What size squares should be cut from the cardboard? Volume = (height)(length)(width) Height = x Length = 25 – 2x Width = 20 – 2x 25 x x 20
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Practice Problems Dixie Packaging Company has contracted to make boxes with a volume of approximately 484 cubic inches. Squares are to be cut from the corners of a 20-in. by 25-in. piece of cardboard, and the flaps folded up to make an open box. What size squares should be cut from the cardboard? Solve the equation: Solve graphically!!! 25 Window: [0, 10] by [0, 1000] x Squares with length in. or in. should be cut from the cardboard x 20
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Practice Problems 2 3, noncollinear
How many points do we need to determine a slant line? How many points do we need to determine a quadratic function? 3, noncollinear In general, we need (n + 1) points positioned with sufficient generality to determine a polynomial function of degree n. The process of fitting a polynomial of degree n to (n + 1) points is called polynomial interpolation.
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Practice Problems PERFECT!!!
Use cubic regression to fit a curve through the four points given in the following table. x –2 1 3 8 y 2 0.5 –0.2 1.25 How good are the fits of these curves??? PERFECT!!! Use quartic regression to fit a curve through the five points given in the following table. x 3 4 5 6 8 y –2 –4 –1 8 3
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Practice Problems U.S. Farm Exports Year Amount (billions) 1980 41.2
Try various polynomial regression models (degrees n = 1, 2, 3, 4) for the given data, and decide which is the best model (let x = 0 be 1980).
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Practice Problems Which is the best???
Try various polynomial regression models (degrees n = 1, 2, 3, 4) for the given data, and decide which is the best model. Linear model: Which is the best??? (think graphically and algebraically) Quadratic model: Cubic model: Quartic model:
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Practice Problems They need between 30 and 541 customers
Economists for Smith Brothers, Inc., find the company profit P by using the formula P = R – C, where R is the total revenue generated by the business and C is the total cost of operating the business. (a) Using data from past years, the economists determined the revenue and cost functions below, where x is the number of customers patronizing the business. How many customers must Smith Bros. have to be profitable each year? Where is this function positive? Graph Window: [–10, 600] by [–1000, ] They need between 30 and 541 customers
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Where is the profit function
Practice Problems Economists for Smith Brothers, Inc., find the company profit P by using the formula P = R – C, where R is the total revenue generated by the business and C is the total cost of operating the business. (b) How many customers must there be for Smith Bros. to realize an annual profit of $60,000? Where is the profit function equal to the line? Graph P(x) with the line y = 60,000 Either 201 or 429 gives a profit slightly over $60,000; 200 or 430 customers both yield slightly less than $60,000
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