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b) The maximum height the ball reaches is the y-coordinate (or h(t)-coordinate) of the vertex. Since the ball attains its maximum height when t 1 2 , fi nd h a1 2 b. ha1 2 b 16 a1 2 b 2 16 a1 2 b 24 16 a1 4 b 8 24 4 32 28 The ball reaches a maximum height of 28 ft. YOU TRY 2 An object is propelled upward from a height of 10 ft. The height h of the object (in feet) t sec after the ball is released is given by h(t) 16t2 32t 10 a) How long does it take the object to reach its maximum height? b) What is the maximum height attained by the object? 3 Write a Quadratic Function to Solve an Applied Problem Involving a Maximum or Minimum Value EXAMPLE 3 Ayesha plans to put a fence around her rectangular garden. If she has 32 ft of fencing, what is the maximum area she can enclose? Solution Begin by drawing a picture. Let x the width of the garden Let y the length of the garden Label the picture. y x x y We will write two equations for a problem like this: 1) The maximize or minimize equation; this equation describes what we are trying to maximize or minimize. 2) The constraint equation; this equation describes the restrictions on the variables or the conditions the variables must meet. Here is how we will get the equations. 1) We will write a maximize equation because we are trying to fi nd the maximum area of the garden. Let A area of the garden The area of the rectangle above is xy. Our equation is Maximize: A xy Read this example slowly and carefully. Be sure you understand everything being done to solve this problem. 670 CHAPTER 10 Quadratic Equations and Functions www.mhhe.com/messersmith


messersmith_power_intermediate_algebra_1e_ch4_7_10
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