MAT135 Review for Test 4 Dugopolski Sections 7.5, 7.6, 8.1, 8.2, 8.3, 8.4 1 1. Use the discriminant to determine the number and type(s) of solutions for 24 8 4 0xx. A. One real solution B. One complex solution C. Two real solutions D. Two complex solutions 2. Simplify: 140. A. 2 35 B. 2 35 C. 2 35i D. 2 35i 3. An object is thrown upward from 96 feet above the ground with an initial velocity of 80 ft/sec. The height of the object, in feet, after t seconds is given by 2( ) 16 80 96h t t t. After how many seconds does the object hit the ground? A. 6.0 seconds B. 11.0 seconds C. 5.0 seconds D. 3.0 seconds 4. If 2( ) 3 and ( ) 12 1, where is ( ) ( )?f x x g x x f x g x A. 12 333 B. 6 393 C. 6 333 D. 6 336 5. Evaluate and write the answer in standard form:975ii. A. 5 i B. 2 i C. 524 24i D. 1713 26iMAT135 Review for Test 4 Dugopolski Sections 7.5, 7.6, 8.1, 8.2, 8.3, 8.4 2 6. Find the domain and range of the graph below. You may assume each tick mark represents one unit. A. Domain ( , ) Range [5, ) B. Domain [5, ) Range ( , ) C. Domain ( , ) Range ( ,5] D. Domain ( ,5] Range ( , ) 7. What is true of 2( ) 2 4?f x x x A. The y-intercept is(0, 4). B. It is a parabola that opens downward. C. The vertex is at (2,4). D. ()fx has no real roots. 8. Simplify: ( 10 2 16) ( 2 2 4). A. 8 12i B. 84i C. 12i D. 12 12i 9. If 2( ) 2 28 and ( ) 18 , where is ( ) ( )f x x g x x f x g x ? A. 2, 7xx B. 2, 7xx C. 7, 2xx D. 7, 2xx y xMAT135 Review for Test 4 Dugopolski Sections 7.5, 7.6, 8.1, 8.2, 8.3, 8.4 3 10. Solve: 5 ( 4) (4 2)( 4)x x x x. A. 2x B. 4x C. 4, 2xx D. 4, 2xx 11. Use the quadratic formula to solve: 210 29 0xx. A. 7, 3xx B. 10 4xi C. 52xi D. 52xi 12. Does 2( ) 4 8 4f x x x open upward or downward, and does it have a maximum or minimum value? A. ()fx opens downward and has a minimum value. B. ()fx opens downward and has a maximum value. C. ()fx opens upward and has a minimum value. D. ()fx opens upward and has a maximum value. 13. If the area of a square is represented by244xx, find an expression for each side. A. 2x B. 2x C. 2( 2)x D. 2( 2)x 14. Solve: 2256y. A. 16, 16 B. 16 C. 16 D. 0, 16 15. What must be added to both sides of the equation 218 20xx to complete the square? A. 0 B. 81 C. 81 D. none of these 16. Solve: 2(4 6) 11t. A. 54t B. 11 6t C. 11 64t D. 11 64tMAT135 Review for Test 4 Dugopolski Sections 7.5, 7.6, 8.1, 8.2, 8.3, 8.4 4 17. What is the range of the function shown below? You may assume that each tick mark represents one unit. A. [3, ) B. [ 3, ) C. ( ,3] D. ( , 3] 18. Solve: ( 9)( 8) 16xx. A. 9, 8xx B. 9, 8xx C. 8, 7xx D. 7, 8xx 19. An object is thrown upward from 96 feet above the ground with an initial velocity of 80 ft/sec. The height of the object, in feet, after t seconds is given by 2( ) 16 80 96h t t t. After how many seconds does the object reach its maximum height? A. 2.5 seconds B. 5.0 seconds C. 5.0 seconds D. 11.0 seconds 20. What is true of 2( ) 2 7f x x x? A. It has a maximum value at( 6, 1). B. It has a minimum value at( 6, 1). C. It has a minimum value at( 1, 6). D. It has a maximum value at( 1, 6). x yMAT135 Review for Test 4 Dugopolski Sections 7.5, 7.6, 8.1, 8.2, 8.3, 8.4 5 21. A rug must fit into a room so that there is a border of equal width on all sides. If the room is 28 feet by 23 feet and the area of the rug is 234 square feet, how wide will the border be? A. 5.0 feet B. 4.5 feet C. 3.5 feet D. 2.5 feet 22. What is the quadratic equation that has roots at 11 and 43xx A. 212 7 1 0xx B. 212 7 1 0xx C. 212 1 0xx D. 212 0xx 23. What are the x-intercepts of2( ) 3 18f x x x? A. (6,0),(3,0) B. (6,0),( 3,0) C. ( 6,0),(3,0) D. ( 6,0),( 3,0) 24. The temperature, t, in degrees Farenheit, of a certain chemical reaction can be approximated by the function 2( ) 3 36 70t s s s, where s is the number of seconds after the reaction begins. What is the lowest temperature possible, and when will it occur? A. The lowest temperature will be 0178 F after 6 seconds. B. The lowest temperature will be 082 F after 12 seconds. C. The lowest temperature will be 038 F after 6 seconds. D. The lowest temperature will be 011 F after 3 seconds. 25. Find the domain and range of 2( ) 2 4 3f x x x A. Domain: ( , ) Range: ( ,5] B. Domain: ( , ) Range: [5, ) C. Domain: ( ,5] Range: ( , ) D. Domain: ( , ) Range: [ 5, ) 26. What is the vertex of 2( ) 4 32 67f x x x? A. ( 4, 3) B. (4,3) C. ( 3, 4) D. (3,4)MAT135 Review for Test 4 Dugopolski Sections 7.5, 7.6, 8.1, 8.2, 8.3, 8.4 6 27. What is the minimum value of the function graphed below? You may assume that each tick mark represents one unit. A. 1y B. 9y C. 2y D. 4y 28. A ball is thrown upward with an initial velocity of 56 ft/sec. The height, in feet, after t seconds is approximated by ( ) (56 16 )h t t t. What is the maximum height attained by the ball? A. 43.6 feet B. 65.3 feet C. 98 feet D. 49 feet 29. 26 2 17 0xx has A. one real solution. B. two real solutions. C. two complex solutions. D. no solution. 30. Use the quadratic formula to solve 22 3 2 5x x x. A. 152x B. 152x C. 15x D. 15x x yMAT135 Review for Test 4 Dugopolski Sections 7.5, 7.6, 8.1, 8.2, 8.3, 8.4 7 31. Which of the following statements is true about 2( ) 9 20f x x x? A. The x-intercepts are (4,0) and ( 5,0). B. The y-intercept is (0, 20). C. The vertex is 91,24. D. Both B and C are true. …