How can two answers be possible? After 7 8 sec the ball is 18 ft above the ground on its way up, and after 1 sec, the ball is 18 ft above the ground on its way down. The ball reaches a height of 18 ft after 7 8 sec and after 1 sec. c) We must determine the amount of time it takes for the ball to hit the ground. When the ball hits the ground, how high off of the ground is it? It is 0 ft high. Find t when h 0. h 16t2 30t 4 0 16t2 30t 4 Substitute 0 for h. 0 8t2 15t 2 Divide by 2. 0 (8t 1)(t 2) Factor. b R 8t 1 0 or t 2 0 Set each factor equal to 0. 8t 1 t 1 8 or t 2 Solve. Since t represents time, t cannot equal 1 8 . We reject that as a solution. Therefore, t 2. The ball will hit the ground after 2 sec. Note In Example 5, the equation can also be written using function notation h(t) 16t2 30t 4 since the expression 16t2 30t 4 is a polynomial. Furthermore, h(t) 16t 2 30t 4 is a quadratic function, and we say that the height, h, is a function of the time, t. We will study quadratic functions in more detail in Chapter 10. YOU TRY 5 An object is thrown upward from a building. The height h of the object (in feet) t sec after the object is released is given by the quadratic equation h 16t2 36t 36 a) What is the initial height of the object? b) How long does it take the object to reach a height of 44 ft? c) How long does it take for the object to hit the ground? ANSWERS TO YOU TRY EXERCISES 1) width 2 ft; length 4 ft 2) 6, 8, 10 or 2, 0, 2 3) 3 4) length of wire 20 ft; height of pole 16 ft 5) a) 36 ft b) 0.25 sec and 2 sec c) 3 sec 408 CHAPTER 7 Factoring Polynomials www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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