46) A ball is thrown upward from a height of 20 feet. The height h of the ball (in feet) t seconds 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 feet? 1.5 sec b) How long does it take the ball to hit the ground? (Hint: When the ball hits the ground, h 0.) 1 16 sec or about 1.72 sec Extension 2 47) What is the discriminant of a quadratic equation? 48) If the discriminant of a quadratic equation is It is the expression under the radical in the quadratic formula, b2 4ac. positive but not a perfect square, what does that tell you about the solutions of the equation? The equation has two irrational solutions. 49) If the discriminant of a quadratic equation is positive and the square of an integer, what does that tell you about the solutions of the equation? The equation has two rational solutions. 50) If the discriminant of a quadratic equation is negative, what does that tell you about the solutions of the equation? The equation has no real number solutions. For each equation, fi nd the value of the discriminant. Then, determine the number and type of solutions of each equation. Do not solve the equation. 51) 2n2 7n 3 0 52) w2 8w 5 0 53) 10p2 9p 3 0 54) 4k2 28k 49 0 55) 3x2 4x 1 56) 3t 1 5t2 57) 9 5h(5h 6) 58) 6(y2 2) y 25; two rational solutions 44; two irrational solutions 39; no real number solutions 0; one rational solution 28; two irrational solutions 11; no real number solutions 0; one rational solution 289; two rational solutions 31) 0.8v2 0.1 0.6v 32) 0.2m2 0.1m 1.5 {0.25, 0.5} {3, 2.5} 33) 16g2 3 0 13 34) 49n2 20 0 2 4 35) 9d 4 0 36) 4k2 25 0 37) 3(3 4r) 4r2 3 e 2 f e f 38) 5y(5y 2) 1 e 13 4 , 215 7 39) 6 7h 3h2 40) 1 t(2 5t) 0 41) 4p2 6 20p 42) 4x2 6x 16 e 5 119 2 , 5 119 2 f , 215 7 e 3 173 4 , 3 173 4 Write an equation and solve. Give an exact answer, and use a calculator to round the answer to the nearest hundredth. 43) The hypotenuse of a right triangle is 1 inch less than twice the shorter leg. The longer leg is 123 inches 2 170 long. Find the length of the shorter leg. 3 in. or about 3.46 in. 44) The hypotenuse of the right triangle is 1 inch more than twice the longer leg. The length of the shorter leg is 114 in. Find the length of the longer leg. 2 143 3 in. or about 1.52 in. Solve. Give an exact answer, and use a calculator to round the answer to the nearest hundredth. 45) An object is thrown upward from a height of 24 feet. The height h of the object (in feet) t seconds after the object is released is given by h 16t2 24t 24 a) How long does it take the object to reach a height of 8 feet? 2 sec b) How long does it take the object to hit the ground? (Hint: When the object hits the ground, h 0.) f f 3 133 4 sec or about 2.19 sec R1) How could you use the quadratic formula to help you factor a more complicated quadratic expression? R2) Do you think some of these exercises could have been solved using another method? Explain. SECTION 10.3 www.mhhe.com/messersmith Solving Quadratic Equations Using the Quadratic Formula 627
messersmith_power_introductory_algebra_1e_ch4_7_10
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