YOU TRY 4 Solve. A wire is attached to the top of a pole. The wire is 4 ft longer than the pole, and the distance from the wire on the ground to the bottom of the pole is 4 ft less than the height of the pole. Find the length of the wire and the height of the pole. Wire Pole Next we will see how to use quadratic equations that model real-life situations. 4 Solve an Applied Problem Using a Given Quadratic Equation EXAMPLE 5 A Little League baseball player throws a ball upward. The height h of the ball (in feet) t sec after the ball is released is given by the quadratic equation h 16t2 30t 4 a) What is the initial height of the ball? b) How long does it take the ball to reach a height of 18 ft? c) How long does it take for the ball to hit the ground? Solution a) We are asked to fi nd the height at which the ball is released. Since t represents the number of seconds after the ball is thrown, t 0 at the time of release. Let t 0, and solve for h. h 16(0)2 30(0) 4 Substitute 0 for t. 0 0 4 4 The initial height of the ball is 4 ft. b) We must fi nd the time it takes for the ball to reach a height of 18 ft. Find t when h 18. h 16t2 30t 4 18 16t2 30t 4 Substitute 18 for h. 0 16t2 30t 14 Write in standard form. 0 8t2 15t 7 Divide by 2. 0 (8t 7)(t 1) Factor. b R 8t 7 0 or t 1 0 Set each factor equal to 0. 8t 7 t 7 8 or t 1 Solve. Try to sketch a picture for this problem. www.mhhe.com/messersmith SECTION 7.5 Applications of Quadratic Equations 407
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