408 CHAPTER 6 Algebra, Graphs, and Functions In Exercises 83 – 86, solve the equation using the quadratic formula. If the equation has no real solution, so state. 83. x x6 16 0 2 − − = −2, 8 84. x x 2 3 0 2 − − = −1, 3 2 85. x x 2 3 4 0 2 − + = No real solution 86. x x3 2 0 2 − − = ± 3 17 2 6.10 In Exercises 87–90, determine whether the graph represents a function. If it does represent a function, give its domain and range. 87. 3 3 23 23 y x Function, domain: = − − x 2, 1, 2, 3; range: = − y 1, 0, 2 88. 6 6 26 26 y x Not a function 89. 3 2 22 23 y x Not a function 90. 15 15 215 215 y x Function, domain: ;R range: R In Exercises 91–94, evaluate f x( ) for the given value of x. 91. f x x x ( ) 4 3, 4 = + = 19 92. f x x x ( ) 2 5, 3 = − + = − 11 93. f x x x x ( ) 3 2 1, 5 2 = − + = 66 94. f x x x x ( ) 4 7 9, 1 2 = − + + = − −2 In Exercises 95 and 96, for each function a) determine whether the parabola will open upward or downward. b) determine the equation of the axis of symmetry. c) determine the vertex. d) determine the y-intercept. e) determine the x-intercepts if they exist. f) graph the function. g) determine the domain and range. 69. MODELING—Minimizing Parking Costs The cost of parking in All-Day parking lot is $5 for the first hour and $0.50 for each additional hour. Sav-a-Lot parking lot costs $4.25 for the first hour and $0.75 for each additional hour. a) In how many hours after the first hour would the total cost of parking at All-Day and Sav-a-Lot be the same? 3 hr b) If Mark needed to park his car for 5 hr, which parking lot would be less expensive? All-Day parking lot 6.8 In Exercises 70 and 71, graph the inequality. 70. x y 2 3 12 + ≤ * 71. x y 4 2 12 + ≥ * In Exercises 72 and 73, graph the system of linear inequalities and indicate the solution set. 72. x y 2 8 + < y x2 1 ≥ − * 73. x y 5 − > x y 6 5 30 + ≤ * 74. The set of constraints and profit formula for a linear programming problem are + ≤ + ≤ ≥ ≥ = + x y x y x y P x y 2 3 12 2 8 0 0 5 3 a) Draw the graph of the constraints and determine the vertices of the feasible region. * b) Use the vertices to determine the maximum and minimum profit. Maximum is 21 at (3, 2); minimum is 0 at (0, 0). 6.9 In Exercises 75–78, factor the trinomial. 75. x x6 9 2 + + + + x x ( 3)( 3) 76. x x2 15 2 + − + − x x ( 5)( 3) 77. x x 10 24 2 − + − − x x ( 6)( 4) 78. x x 6 7 3 2 + − − + x x (3 1)(2 3) In Exercises 79–82, solve the equation by factoring. 79. x x9 20 0 2 + + = 4, 5 − − 80. x x3 10 2 + = −5, 2 81. x x 3 17 10 0 2 − + = 2 3 , 5 82. x x 3 7 2 2 = − − − − 2, 1 3 $ *See Instructor Answer Appendix
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