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Algebra 2 Thanksgiving Holiday Extra Credit Name_________________________ Pd____________ **Complete this ENTIRE WORKSHEET (Do Not Leave any blank) over the Holiday Break and turn in by 8:40am on 11/28/16 to receive up to 20 bonus points on the Unit 4 test based on how many you answer correctly and show work!! You must Show all WORK to be graded! IT WILL NOT ACCEPT TED LATE... (Unless you have talked to me prior to the break). Problems with a code (NW) require No Work. All others require you to show work!! 1. Graph each parent function on the grid above the equation. (NW) 10 10 8 8 6 6 4 4 2 2 -10 -8 -6 -4 -2 y 2. 2 4 6 8 10 -10 -8 -6 -4 -2 -2 -2 -4 -4 -6 -6 -8 -8 -10 -10 3 2 4 6 8 10 2 4 6 8 10 y 2x x Graph each parent function on the grid above the equation. (NW) 10 10 8 8 6 6 4 4 2 2 -10 -8 -6 -4 -2 y 2 4 6 8 10 -10 -8 -6 -4 -2 -2 -2 -4 -4 -6 -6 -8 -8 -10 -10 y x Pg 1 of 12 1 x 3. Answer the following questions about the parent functions we studied. Write the name of the function that meets the criteria asked: (NW) a. Origin symmetry and No x-intercept. _________________________ b. Domain (0, ) and Range (, ) . _________________________ c. y-intercept (0,1) _________________________ d. Domain is same as Range, with No symmetry _________________________ 4. Given the following solution graphed on the number line, write the solution in both Inequality Notation and Interval Notation. (NW) Inequality Notation (INQ): _________________________________________________ Interval Notation (INT): ___________________________________________________ 5. Given the graph, write the domain and range in both formats. (NW) Domain (INT): __________________________________ Domain (INQ): _________________________________ Range (INT): ___________________________________ Range (INQ): ___________________________________ Pg 2 of 12 6. Given the function f(x). LIST all the transformations in the correct order to f(x). (NW) Function Transformations (In Order) a. 4 f ( x 3) 2 b. 1 f ( x 8) 5 3 1 c. f ( x 2) 7 2 d. 7. 4 f (4 x 4) 4 Given the graph of h(x) on the left grid, graph f(x) on the right grid using transformations. (2) NW f ( x) 2h( x 3) 1 h( x ) Pg 3 of 12 8. Given the graph of h(x) on the left grid, graph f(x) on the right grid using transformations. (2) NW f ( x) h(2 x 2) 1 h( x ) 9. Find the inverse of the following function. Write your answer in the correct format if the inverse is a function or not. (2) f ( x) 3x 8 Inverse: ___________________________________ 10. Find the inverse of the following function. Write your answer in the correct format if the inverse is a function or not. (2) f ( x) x 2 25 Inverse: ______________________________________________________ Pg 4 of 12 11. Given the following graph of f(x), answer the following questions (a –c). There are no decimal answers. (NW) a. f (7) ________ b. f (1) ________ c. f (9) ________ 12. Given the following functions f(x) and g(x) below, answer the questions (a – c) f ( x) 6 x 4 a. g ( x) x 2 2 x b. g ( 2) f (3) c. f ( g (3)) 13. Given the following functions f(x) and g(x) below, answer the questions (a – b). (2) f ( x) 2 x 7 g ( x) 9 x 2 a. Find (f g )(3) b. Find Pg 5 of 12 ( g f )( x) 14. For the following equations, list the transformations on the line to assist you in graphing. Then graph the equations with the transformations. Plot all points that will fit on the 10x10 grid. (2) NW a. y 2 | x 4 | 3 Transf: _________________________ b. y 2 x 4 7 Transf: ____________________________ Pg 6 of 12 Solve each absolute value equation below. Check your answers for extraneous solutions. Show all steps and work. Circle or box your final answers. (2) 15. x 4 16 10 16. 3 x 3 4 44 Solve each absolute value inequality and then graph the solution set on the number line. Check for extraneous solutions. (2) 17. 2 x 4 2 16 Solution: ___________________________ 18. 2 | x 4 | 8 42 Solution: ______________________________ Pg 7 of 12 Questions 19-24: Factor the following quadratic equations. If it doesn’t factor, write Prime. NW 19. x2 – 13x – 48 20. 16x2 – 1 21. 12x2 – 3x Factors: ____________________ Factors: _____________________ Factors: __________________ 22. 12x2 – x – 1 23. x2 – 7x + 6 24. 12 x 2 16 x 3 Factors: _________________ Factors: _________________ Factors: _________________ Questions 25-27. Simplify the following radical expressions: BOX your final answer!! 25. 28 26. 4 18 Pg 8 of 12 27. 6 48 Questions 28-31. Simplify the following complex number expressions: BOX your final answer!! (2) 28. (7 4i) (12 11i) 29. (5 9i) (13 12i) 30. (7 4i)(7 4i) 31. (6 2i )(5 9i) Questions 32-34: Solve the following quadratic equations by the Square Roots method! Final answers should be simplified radical. Put answers in box. (2) 32. 2x2 + 10 = 16 33. 3(x + 2)2 + 5 = -13 Pg 9 of 12 34. (x – 4)2 – 6 = 22 Questions 35-37: Solve the following quadratic equations by Completing the Square. Answers should be simplified radical format. Put answers in box. (2) 35. x2 – 8x - 24 = 0 36. 2x2 – 16x + 44 = 0 37. x2 – 2x = 8 Questions 38-40: Solve the following quadratic equations using the quadratic formula. x b b2 4ac 2a Solve using the quadratic formula. Show all work! Reduce radicals if possible. Put final answers in the box! (2) 38. 3x2 + 6x = -2 39. 6x2 – 8x + 3 = 0 Pg 10 of 12 40. 2x2 – x = -6 41. A rocket is fired at an angle and its path is modeled by the equation below. In the equation below “h” is height in feet and “x” is horizontal distance in feet. Answer the questions below, using correct units on answers. Round answers to 1 decimal place. (NW) h .0023x 2 4.65 x 5.3 a. What was the maximum height of the rocket? b. At what horizontal distance did the rocket hit the ground from where it was launched? c. At what horizontal distances from launch was the rocket exactly 500 feet above the ground? d. What was the height of the rocket before it was fired into the air? e. If there was a 100 feet high wall positioned 2000 feet horizontally from the rocket launch, would the rocket make it over the wall? Explain your answer. Questions 42-43: Graph the following quadratic inequalities. Then state the solution for each in Interval Notation(INT). (2) (NW) 42. y < -x2 – 5x + 3 43. y ≥ 2x2 + 3x - 6 10 10 8 8 6 6 4 4 2 2 -10 -8 -6 -4 -2 2 4 6 8 10 -10 -8 -6 -4 -2 2 -2 -2 -4 -4 -6 -6 -8 -8 -10 -10 Solution: _______________________ 4 6 8 10 Solution: _________________________ Pg 11 of 12 Questions 44-45: Solve the Quadratic Inequalities below and graph your solutions on the number line provided. Then write final solution in Interval Notation!!. Round to 1 decimal place. (2) NW 44. 2x2 – x – 6 > 0 45. x2 – 6x ≤ 27 Soln: _______________________ Soln: ___________________________ Questions 46-47: Given the following 2 functions, prove whether or not they are inverses of one another using composition. Show all work. (2) 46. f ( x) 2 x 6 f ( x) x 14 47. g ( x) 14 x Pg 12 of 12 g ( x) 1 x 3 2