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ALGEBRA II WS 209 NAME _____________________________ PERIOD _____ DATE ________________ TRUE OR FALSE. NO NEED TO CORRECT THE FALSE. ____False______________1. All rational numbers are also integers. _____True_____________2. (7 + 3i) + (8 – 2i) = (8 – 2i) + (7 + 3i) is the commutative property of complex numbers. _____False_____________3. Graphing a quadratic function can always provide the exact roots of the function. _____False_____________4. ( m – 6)2 = m2 + 36. _____False_____________5. The graph of y = x is a vertical line. CIRCLE THE BEST ANSWER. 6. The irrational number: 7. The conjugate of 6 – 5i: 81 or 48 -6 + 5i or 6 + 5i 8. If a quadratic has a double root, what is true about the number of solutions? One real Solution or 9. Synonym for the roots of a quadratic equation: Two real Solutions x-intercepts or 10. A quadratic function with roots of 5 and –2: y = (x + 5)(x – 2) or PERFORM THE OPERATIONS WITHOUT A CALCULATOR: 11. i6 12. (-2 – 5i) + (8 – 10i) 6-15i -1 15. (4 + 5i)2 -9+40i 4i 3 y = (x – 5)(x + 2) 13. (3 + 6i) – (-5 – 10i) 8+16i 14. (5 + 2i)(3 – 7i) 29-29i 17. y-intercepts 48 18. 3i 5 45 3 2i 4 5i 22 + 23i 41 16. 19. 7 3 12 75 FIND THE DISCRIMINANT OF THE FOLLOWING AND DESCRIBE THE NATURE OF THE SOLUTIONS. 20. x2 + 2 = 3x 1, 2 solutions 21. 3x2 = 7x + 8 -47, no real solutions -----------------------------------------------------------------------------------------------------------SOLVE AND CHECK EACH OF THE FOLLOWING: WORK MUST BE SHOWN! 22. x2 + 2x2 + 1 = -1 – x -1 ± i 23 6 24. 2x2 + 20x – 22 = 0 x=-11, 1 2x2 – 7x – 4 = 0 x=-0.5, 4 23. 10x – 6 = 5x2 5±i 5 x= 5 25. 26. The manager of a factory has found that the output at the factory can be modeled be the function T(n) = -0.2n2 + 8n – 24, where n is the number of workers at the factory on a given day and T(n) is the output. a. b. 56 Find the number of workers needed in order to maximize the output. (Two points) 20 What is the maximum output at this factory? (Two points) 27. A football is thrown by a quarterback and follows the path given by h ( x ) = -0.0095x 2 + x + 7 , where h is the height of the ball in feet and x is the horizontal distance the ball has traveled in fet. If any height less than 10 feet can be caught or knocked down, at what distances from the quarterback can the ball be knocked down? X<3.09 feet or x> 102.1 feet 28. A buisness offers tours to the Amazon. The profit, P, that the company earns for x number of tourists can be modeled by P ( x ) = -25x 2 +1000x - 3000 . How many people are needed for a profit of at least $5000? 11.06 £ x £ 28.94 29. Lisa has a swimming pool that is 60 ft. by 20 ft. She wants to put a sidewalk around it of uniform width. Lisa lives in the country, but she only want the total area taken up to be 2000 sq. ft. How wide should the sidewalk be? X= 4.49 feet 30. Solve 2x - 8 = 7 X=15/2, x= 1/2