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7) Let f (x) ax2 bx c. How do you know whether the function has a maximum or minimum value at the vertex? 8) Is there a maximum value of the function y 2x2 12x 11? Explain your answer. For Problems 9–12, answer parts a)d) for each function, f(x). a) Does the function attain a minimum or maximum value at its vertex? b) Find the vertex of the graph of f(x). c) What is the minimum or maximum value of the function? d) Graph the function to verify parts a)–c). 9) f (x) x2 6x 9 10) f (x) x2 2x 4 11) f(x) 1 2 x2 4x 6 12) f (x) 2x2 4x Objective 2: Given a Quadratic Function, Solve an Applied Problem Involving a Maximum or Minimum Value Solve. 13) An object is fi red upward from the ground so that its height h (in feet) t sec after being fi red is given by h(t) 16t2 320t a) How long does it take the object to reach its maximum height? b) What is the maximum height attained by the object? c) How long does it take the object to hit the ground? 14) An object is thrown upward from a height of 64 ft so that its height h (in feet) t sec after being thrown is given by h(t) 16t2 48t 64 a) How long does it take the object to reach its maximum height? b) What is the maximum height attained by the object? c) How long does it take the object to hit the ground? 15) The average number of traffi c tickets issued in a city on any given day SundaySaturday can be approximated by T(x) 7x2 70x 43 where x represents the number of days after Sunday (x 0 represents Sunday, x 1 represents Monday, etc.), and T(x) represents the number of traffi c tickets issued. On which day are the most tickets written? How many tickets are issued on that day? 16) The number of guests staying at the Toasty Inn from January to December 2013 can be approximated by N(x) 10x2 120x 120 where x represents the number of months after January 2013 (x 0 represents January, x 1 represents February, etc.), and N(x) represents the number of guests who stayed at the inn. During which month did the inn have the greatest number of guests? How many people stayed at the inn during that month? 17) The number of babies born to teenage mothers from 1989 to 2002 can be approximated by N(t) 0.721t2 2.75t 528 where t represents the number of years after 1989 and N(t) represents the number of babies born (in thousands). According to this model, in what year was the number of babies born to teen mothers the greatest? How many babies were born that year? (U.S. Census Bureau) 18) The number of violent crimes in the United States from 1985 to 1999 can be modeled by C(x) 49.2x2 636x 12,468 where x represents the number of years after 1985 and C(x) represents the number of violent crimes (in thousands). During what year did the greatest number of violent crimes occur, and how many were there? (U.S. Census Bureau) Objective 3: Write a Quadratic Function to Solve an Applied Problem Involving a Maximum or Minimum Value Solve. 19) Every winter Rich makes a rectangular ice rink in his backyard. He has 100 ft of material to use as the border. What is the maximum area of the ice rink? 20) Find the dimensions of the rectangular garden of greatest area that can be enclosed with 40 ft of fencing. 678 CHAPTER 10 Quadratic Equations and Functions www.mhhe.com/messersmith


messersmith_power_intermediate_algebra_1e_ch4_7_10
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