YOU TRY 3 Find the value of the discriminant. Then, determine the number and type of solutions of each equation. a) 2x2 x 5 0 b) m2 5m 24 c) 3v2 4v 1 d) 4r(2r 3) 1 6r r2 4 Solve an Applied Problem Using the Quadratic Formula EXAMPLE 4 A ball is thrown upward from a height of 20 ft. The height h of the ball (in feet) t sec after the ball is released is given by h 16t2 16t 20 a) How long does it take the ball to reach a height of 8 ft? b) How long does it take the ball to hit the ground? Solution a) Find the time it takes for the ball to reach a height of 8 ft. Find t when h 8. h 16t2 16t 20 8 16t2 16t 20 Substitute 8 for h. 0 16t2 16t 12 Write in standard form. 0 4t2 4t 3 Divide by 4. t b 2b2 4ac 2a Quadratic formula (4) 2(4)2 4(4)(3) 2(4) 4 116 48 8 Substitute a 4, b 4, and c 3. Perform the operations. 4 164 8 4 8 8 t 4 8 8 or t 4 8 8 The equation has two rational solutions. t 12 8 3 2 or t 4 8 1 2 Because t represents time, t cannot equal 1 2 . We reject that as a solution. Therefore, t 3 2 sec or 1.5 sec. The ball will be 8 ft above the ground after 1.5 sec. www.mhhe.com/messersmith SECTION 10.2 The Quadratic Formula 629
messersmith_power_intermediate_algebra_1e_ch4_7_10
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