Algebra II Semester Exam Review Sheet

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1 Name: Class: Date: ID: A Algebra II Semester Exam Review Sheet 1. Translate the point (2, 3) left 2 units and up 3 units. Give the coordinates of the translated point. 2. Use a table to translate the graph 3 units to the left. Use the same coordinate plane as the original function. 3. Identify the parent function for g( x) = ( x + 3) 3 and describe what transformation of the parent function it represents. 4. Graph the data from the table. Describe the parent function and the transformation that best approximates the data set. x y Let g(x) be the transformation, vertical translation 3 units down, of f(x) = 4x + 8. Write the rule for g(x). 6. Let g( x) be a vertical shift of f( x) = x up 4 units followed by a vertical stretch by a factor of 3. Write the rule for g( x). 7. The data set shows the amount of funds raised and the number of participants in the fundraiser at the Family House organization branches. Make a scatter plot of the data with number of participants as the independent variable. Then, find the equation of the line of best fit and draw the line. Family House Fundraiser Number of participants Funds raised ($)

2 8. An automotive mechanic charges $50 to diagnose the problem in a vehicle and $65 per hour for labor to fix it. a. If the mechanic increases his diagnostic fee to $60, what kind of transformation is this to the graph of the total repair bill? b. If the mechanic increases his labor rate to $75 per hour, what kind of transformation is this to the graph of the total repair bill? c. If it took 3 hours to repair your car, which of the two rate increases would have a greater effect on your total bill? 9. Using the graph of f(x) = x 2 as a guide, describe the transformations, and then graph the function g(x) = (x + 6) Find the minimum or maximum value of f(x) = x 2 2x 6. Then state the domain and range of the function. 11. Find the zeros of the function h( x) = x x + 60 by factoring. 12. Solve the equation x 2 = 3 2x by completing the square. 13. Express 8 84 in terms of i. 14. Find the zeros of the function f(x) = x 2 + 6x

3 15. Consider the function f(x) = 4x 2 8x Determine whether the graph opens upward or downward. Find the axis of symmetry, the vertex and the y-intercept. Graph the function. 16. Solve the equation 2x = Find the zeros of f(x) = x 2 + 7x + 9 by using the Quadratic Formula. 18. Find the number and type of solutions for x 2 9x = Subtract. Write the result in the form a + bi. (5 2i) (6 + 8i) 20. Multiply 6i( 4 6i). Write the result in the form a + bi. 21. Simplify 2 + 2i 5 + 3i. 3

4 22. Identify the degree of the monomial 5r 3 s Rewrite the polynomial 12x x 5 + 3x 3 + 7x 4 5x in standard form. Then, identify the leading coefficient, degree, and number of terms. Name the polynomial. 24. Add. Write your answer in standard form. (5a 5 a 4 ) + (a 5 + 7a 4 2) 25. Find the product ( 5x 3)(x 3 5x + 2). 26. Divide by using long division: (5x + 6x 3 8) (x 2). 27. Divide by using synthetic division. (x 2 9x + 10) ( x 2) 28. Write an expression that represents the width of a rectangle with length x + 5 and area x x x Make sure you study your vocabulary that is on your Semester Exam Review Learning Objective Sheet. 4

5 Algebra II Semester Exam Review Sheet Answer Section 1. ANS: TOP: 1-1 Exploring Transformations 2. ANS: TOP: 1-1 Exploring Transformations 3. ANS: The parent function is the cubic function, f( x) = x 3. g( x) = ( x + 3) 3 represents a horizontal translation of the parent function 3 units to the left. TOP: 1-2 Introduction to Parent Functions 1

6 4. ANS: Square root function translated 3 units to the left. TOP: 1-2 Introduction to Parent Functions 5. ANS: g(x) = 4x + 5 TOP: 1-3 Transforming Linear Functions 6. ANS: g( x) = 3x + 12 TOP: 1-3 Transforming Linear Functions 7. ANS: y = 8.5x ; r 0.66 TOP: 1-4 Curve Fitting with Linear Models 8. ANS: a. Vertical translation up 10 b. Horizontal compression by 13/15 or c. The increase in labor rate. 2

7 9. ANS: g(x) is f(x) translated 6 units left and 2 units down. TOP: 2-1 Using Transformations to Graph Quadratic Functions 10. ANS: The minimum value is 7. D: {all real numbers}; R: {y y 7} TOP: 2-2 Properties of Quadratic Functions in Standard Form 11. ANS: x = 20 or x = 3 TOP: 2-3 Solving Quadratic Equations by Graphing and Factoring 12. ANS: x = 1 or x = 3 TOP: 2-4 Completing the Square 13. ANS: 16i 21 TOP: 2-5 Complex Numbers and Roots 14. ANS: x = 3 + 3i or 3 3i TOP: 2-5 Complex Numbers and Roots 3

8 15. ANS: The parabola opens downward. The axis of symmetry is the line x = 1. The vertex is the point ( 1,14). The y-intercept is 10. TOP: 2-2 Properties of Quadratic Functions in Standard Form 16. ANS: x = ±3i TOP: 2-5 Complex Numbers and Roots 17. ANS: x = 7 ± 13 2 TOP: 2-6 The Quadratic Formula 18. ANS: The equation has two real solutions. TOP: 2-6 The Quadratic Formula 19. ANS: 1 10i TOP: 2-9 Operations with Complex Numbers 20. ANS: i TOP: 2-9 Operations with Complex Numbers 21. ANS: i TOP: 2-9 Operations with Complex Numbers 4

9 22. ANS: 8 TOP: 3-1 Polynomials 23. ANS: 7x 5 + 7x 4 + 3x x 2 5x + 6 leading coefficient: 7; degree: 5; number of terms: 6; name: quintic polynomial TOP: 3-1 Polynomials 24. ANS: 6a 5 + 6a 4 2 TOP: 3-1 Polynomials 25. ANS: 5x 4 3x 3 25x x 6 TOP: 3-2 Multiplying Polynomials 26. ANS: 6x x (x 2) TOP: 3-3 Dividing Polynomials 27. ANS: x x 2 TOP: 3-3 Dividing Polynomials 28. ANS: x 2 + 7x + 12 TOP: 3-3 Dividing Polynomials 29. ANS: Study vocabulary. 5

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