<p>Algebra II Fall Semester Final Review Dec. 2011 Name ______</p><p>Unit 1</p><p>Match the parent functions with the graphs and write the name, domain, and range under each graph. a. y= x3 b. y= x c. y= x d. y= x 1 e. y= x2 f. y = g. y= ex h. y= log x x</p><p>1. 2. 3. 4. </p><p>5. 6. 7. 8. </p><p>Identify the parent function of the following:</p><p>1 3 2 9. f( x )= - 6 10. f( x )= 5( x - 2) 11. f( x )= - x + 4 12. f( x )= 5log( x + 2) - 3 x + 5 3</p><p>Find the inverse of the given relations:</p><p>13. {(2,1) ,( 3,- 1) ,( 4,5) ,( 5,1)} 14. 5 1</p><p>2 2</p><p>-3</p><p>15. To find the inverse of a graph, reflect across ______.</p><p>Find the equation of the inverse. 4 5 16. y= -4 x + 1 17. y=2 x2 + 3 18. y = 19. y= x -1 x - 5 4</p><p>Unit 2 y = a (x - h) + k </p><p>How does each transform the graph? a - ______, h - ______, k - ______</p><p>Identify the parent function and describe the transformations: 1 1 1. f( x )= + 3 2. f( x ) = - x2 3. f( x )= - x + 3 - 7 x 2</p><p>1 4. f( x )= - 4 x + 8 5. f( x )= ( x - 7)2 - 2 6. f( x )= 3 x3 - 2 2</p><p>Unit 3 – Curve Fitting 1 – 3: Use the data provided in the table to answer each question. x - 1 0 1 2 3 y 10 8 6 4 2</p><p>1) What is the slope of the linear function? 2) What will the value of y be when x is 10?</p><p>3) Write the equation that represents the equation of best fit. 4) What is the correlation coefficient?</p><p>5 – 7: Use the data provided in the table to answer each question. x - 1 0 1 2 3 y - 6 - 5 - 2 3 10</p><p>5) Use finite difference to determine the type of polynomial function 6) Write the equation of best fit.</p><p>7) What would be the value of y when x = 8? The table provided shows personal income of Americans from 1998 – 2003. Let x = 0 represent the year 1990. Year Amount (trillions of dollars) 1998 7.4 1999 7.8 2000 8.4 2001 8.7 2002 8.9 2003 9.2 (Source: U.S. Census Bureau. Statistical Abstract of the United States. 2004 -2005)</p><p>8) Assume the data is represented by a linear function. Write the equation of best fit.</p><p>9) Find the correlation coefficient.</p><p>Unit 4a – Writing & Graphing Systems Write the system of equations. Don’t solve!</p><p>1. Your teacher gives you a test worth 100 points with 34 questions. Each question is worth either 2 points or 4 points. Write a system of equations to determine the number of 2 point and 4 point questions on the test.</p><p>2. Tom bought 12 student tickets and 4 adult tickets to the football game for $56. Renee bought 4 student tickets and 8 adult tickets for $52. Write the system of equations that will determine the cost of adult tickets and the student tickets that they bought.</p><p>Use graphing to solve each system of equations. </p><p>1. 3x - 4y = 20 y - 2x = 0 </p><p>Rules for graphing inequalities: < > ≤ ≥ </p><p>Line:</p><p>Shade:</p><p>2. Graph the system of inequalities.</p><p> y�3 x 5 1 y< - x + 4 2</p><p>3. Which inequality best describes the graph shown below? 3 A y > − x + 5 4 4 B y < − x + 5 3 3 C y < − x + 5 4 4 D y > − x + 5 3</p><p>2003 Exit 4. Which graph best represents all the pairs of numbers (x, y) such that x + y < −6? F G H J</p><p>Unit 4b – Solving Systems by Substitution & Elimination</p><p>1. Explain what the following terms mean: A. Independent system B. Inconsistent system C. Dependent system</p><p>Solve by substitution: y= 6 x -3x - y = - 1 2. 3. x+ y = 28 2x+ 3 y = 24</p><p>Solve by the elimination method. 3x+ 2 y = 7 -3x + 5 y = 45 4. 5. 5x- 2 y = 1 3x+ 13 y = 9</p><p>6. In the system of equations 4x + 2y = 10 and 3x + 7y = -18, which expression can be correctly substituted for y in the equation 3x + 7y =-18? (A) 10 – 2x (B) 10 + 2x (C) 5 – 2x (D) 5 + 2x</p><p>7. Use substitution or elimination to solve these equations. Show your work 6x + y = -2 6x + 2y = 2 8. Use substitution to determine if the given ordered pair is a solution for the system of equations. 轾y= -2 x (-4,8) 犏 臌3x+ y = - 4</p><p>9. Juan bought 40 drinks, all either cola or root beer. The cola was equal to four times the number of cans of root beer. Write a system of equations to determine the number of cans of cola and root beer he bought. Then solve using the best method.</p><p>10. At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. Write a system to determine t, the cost of a taco, and m, the cost of a small glass of milk. Then solve.</p><p>11. The price, e, of an entertainment system at Extreme Electronics is $220 less than twice the price, u, of the same system at Ultra Electronics. The difference in price between the system at Extreme Electronics and Ultra Electronics is $175. Which system of linear equations can be used to determine the price of the system at each store? (A) 2e – u = 220 (B) 2e – u = 220 (C) 2e – 2u = 440 (D) e – 2u = -220 e – u = -175 e + u = 175 e – u = -175 e – u = 175</p><p>12. Solve the system you chose from #11 with your best method. Write your solution as an ordered pair.</p><p>Unit 5 – Intro to Quadratics</p><p>To find axis of symmetry: To find vertex:</p><p>Find the axis of symmetry and vertex of the following. Show your work!!!</p><p>1. 2x2 – 4x + 5 2. x2 + 6x – 7 </p><p>Find the roots/x-intercepts/zeros/solutions when y=0 from the graphs and tables below. (Write answer in ordered pair(s).)</p><p>3. 4. x y -3 1 -2 0 -1 1 0 4 -1 9 -2 16 Find the following information for the given equation. 5. y = ¾ (x + 2)2 - 3</p><p>Opens:</p><p>AOS:</p><p>Vertex:</p><p>X-intercepts: 6. A ball is tossed straight up at a velocity of 64 ft/sec. The path of the ball is straight up and down. The height of the ball above the ground is modeled by the function h(x) = - 16 x 2 + 64 x. (Use your calculator to graph the path of the ball. Identify what you see a. Line of Symmetry: ______b. Coordinates of the vertex:______c. Roots or Solutions:______d. y-intercept:______</p><p> e. What are the coordinates for the maximum height of the ball? Write as an ordered pair </p><p> f. What is the height of the ball at 3 seconds?______</p><p> g. Write the coordinates that represent the ball reaching the ground. ______</p><p> h. Explain what the x values represent in real life. ______</p><p> i. Explain what the y values represent in real life. ______</p><p>Unit 6– Factoring </p><p>Factor the following completely. Remember all types: split the middle, difference of squares, sum and difference of cubes, and grouping.</p><p>1. x2 – 5x + 6 2. x2 + 8x + 15 3. x2 – 25 4. x3 – 8 </p><p>5. 64x3 + 125 **6. 3xy + 15 – 4y – 20 7. 16x2 – 4 8. x2 + 9x + 20</p><p>9. 4x2 – 35x + 49 10. 8x2 + 10x – 3 11. 5x2 + 19x + 12 12. x2 – 7x – 30 </p><p>Complete the square of the following:</p><p>13. x2 – 6x + ______= 16 + ______14. x2 + 16x + ______= -39 + ______Unit 7 – Solving Quadratic Equations</p><p>Find the solutions to the following quadratic functions.</p><p>1. x2 – 1 = 0 2. x2 + 9x +14 = 0 3. x2 + 14x + 49 = 0</p><p>4. 5x2 + 7x + 2 = 0 5. 9x2 – 6x + 1 = 0 6. 4x – 12 = 0</p><p>Find the equation given the roots/zeros/x-intercepts:</p><p>7. x = -3, x = 5 8. x = -1/4, x = 2 9. x = 1/3, x = -7</p><p>For each question, identify the type and number of roots using the discriminant and then solve to find the roots.</p><p>10) -x2 - 5x + 6 11) 8x2 + 10x – 3 # roots: # roots: Type: Type: Solution: Solution:</p><p>12) 3x2 − 4x – 1 # roots: Type: Solution:</p><p>Solve the following by completing the square. 13. x2 – 2x – 8 = 0 14. 2x2 + 16x = 18 15. x2 – 10x = 10 Unit 8 – Real World Applications of Quadratics</p><p>1 – 3 A ball is tossed straight up at a velocity of 64 ft/sec. The path of the ball is straight up and down. The height of the ball above the ground is modeled by the function h(t) = -16t2 + 64t. (Use your calculator to graph the path of the ball. Identify what you see on your calculator screen by finding the following. You can also use your table.)</p><p>1. What is the maximum height of the ball?______</p><p>2. How long does it take for the ball to reach its maximum height?______</p><p>3. How long until the ball lands?______</p><p>Unit 9 – Quadratic Forms</p><p>1) Describe the transformation of the given quadratic as compared to y = x2: y = -2(x + 1)2 – 4</p><p>2) Place the functions in order from the widest to the narrowest. y = 2x2 y = x2 y = -5x2 y = 0.3x2</p><p>3) Graph y = -(x + 2)(x – 3) 4) Convert y = -5(x + 2)(x – 1) into standard form.</p><p>5) Convert y = x2 – 5x – 6 into factored form. 6) Convert y = x2 + 8x – 10 into vertex form.</p><p>7) Find the length of the base and height of a triangle if the base is 2x + 4 and the height is x – 6 having an area of 48 u2.</p>