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Algebra 1 Name: _______________________________________ Hour: June 2014 Semester 2 Final Exam Review Directions: Show all your work to receive full credit. The question numbers that are circled should be completed without a calculator. Chapter 10: 1.) Multiple Choice: How would you translate the graph of A. Translate the graph of y x 2 B. Translate the graph of y x 2 left 4 units y x 2 up 4 units 2 down 4 units C. Translate the graph of D. Translate the graph of y x y 3 x 2 y x 2 to produce the graph of right 4 units 2.) Graph the function. 3.) Describe how the graph of each function below compares to the graph of a.) 1 1 y 0.5x 2 b.) y x2 4.) How should the graph of 5.) Find the vertex and the axis of symmetry of the parabola. 6.) Graph the quadratic equation y 3x 2 6 x 9 . Identify the vertex, y-intercept, and the zeros of the function when you graph the function. y x2 . y 9x 2 change in order to produce the graph of y x2 8 ? y 2x 2 4 x 6 1 1 y x 2 4 ? Algebra 1 Review 7.) page 2 y x 2 4 x 4 Multiple Choice: Which graph below represents the quadratic equation List the solution(s) to the equation x 2 4 x 4 0 : A. 8.) B. 49 49 , 36 36 B.) 36 36 , 49 49 C.) 6 6 , 7 7 7 7 , 6 6 b.) x 2 3 17 c.) 4 x 2 120 120 Solve each equation. Round the solutions to the nearest hundredth. a.) 5x 2 75 b.) 7x 2 4 100 11.) Solve the equation by completing the square. x 2 6x 3 0 12.) Find the value of c that makes the expression a perfect square trinomial. c.) 3x 6 2 33 b.) x2 22x c a.) x 2 18x c 13.) D.) Find all solutions to each quadratic equation a.) x 2 9 10.) D. Multiple Choice: Find all solutions to the quadratic equation. 49x 2 36 0 A.) 9.) C. Use the Quadratic Formula to solve the equation. Round your solution to the nearest hundredth, if necessary. a.) x 2 2x 1 0 b.) 2x2 x 1 c.) 3x 2 x 3 0 Algebra 1 Review page 3 14.) Multiple Choice: Use the discriminant to find the number of real solutions to the equation 3x 2 3x 4 0 . A. No real solutions B. Not Enough Information C . Two real solutions D. One real solution 15.) Use the discriminant to determine the number of real solutions of each equation. a.) 2x 2 6x 2 0 b.) 4x 2 3x 7 0 c.) 5x 2 3x 1 0 d.) 9x 2 30x 25 0 16.) Multiple Choice: The table gives the number of inner tubes, I, sold in a bike shop between 1985 and 1990. Determine which model best fits the data. Year, t Inner tubes, I 1985 40 1986 56 A. Absolute Value B. Exponential 1987 72 1988 88 1989 104 C. Linear D. Quadratic In 17-23, a.) Tell whether the table of values represents a linear, exponential, or quadratic function. b.) Write an equation for the function. 17.) x y –2 –1 4 9 4 3 18.) x y –2 1 –1 7 19.) x y –2 11 –1 10 20.) x y –1 3 0 0 21.) x y 0 –5 1 –2 22.) x y 1 1 2 2 23.) x y –2 18 –1 14 0 4 1 12 2 36 0 13 1 19 2 25 0 9 1 8 1 3 2 12 3 27 3 4 4 7 2 1 3 4 0 10 2 7 4 8 5 16 1 6 2 2 1990 120 Algebra 1 Review page 4 Chapter 11 2.) Graph the function f (x) x 1 1.) Graph the function f (x) x 1 Domain: ____________ Range: ____________ Domain: ____________ Range: ____________ 1 1 1 1 3.) Graph the function y x 2 3 4.) Domain: ____________ Range: ____________ Graph the function y x 3 2 Domain: ____________ Range: ____________ 1 1 1 1 5.) Simplify: 10 4 a.) 200 b.) 20 c.) d.) 6 20 e.) 9 4 f.) 7 6 8 6 3 6 g.) 32 72 h.) 5 5 i.) 5 5 3 36 2 80 Algebra 1 Review page 5 6.) Solve each equation. Check for extraneous solutions. a.) x 3 6 b.) x 8 8 2 c.) 6 x 4 25 d.) x 72 x e.) 2x 7 5 f.) 1 2x 4 g.) 2x 2x h.) 5 x 30 0 i.) 2x 1 5x 32 7.) Multiple Choice: Find the midpoint of (4, 16) and (9, –2). A. 5 17 , 2 2 D. 13 , 14 B. 13 ,14 13 E. , 7 2 C. 7 10 , 2 F. 5 , 9 2 8.) Find the midpoint of (2, –2) and (–2, –14). 9.) Find the distance between the two points. a.) (–4, –2), (2, 3) b.) (–5, 3), (4, –1) 10.) Find the distance and the midpoint of the segment with endpoints C(8,4) and G(2,3) .