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Algebra 2 Final Name: ___________________________________ Equivalence: I. During our study of quadratic and piecewise - absolute value functions in the first semester we studied manipulation of expressions and equations into different forms. Demonstrate your understanding of these different forms and the reason why you would make the conversion. Factored Standard Vertex Changing Linear Absolute value Forms: Piecewise Quadratic Absolute value II. We also studied the use of various number systems and arithmetic operations. Demonstrate your understanding of these systems and operations – including the use of rational exponents. Discuss how operations with non-real complex numbers is similar to operations with binomials. Number systems: Natural Whole Integers Real – rational & Irrational Complex Arithmetic operations: Addition Subtraction Multiplication Division Raising to a power Analyzing and Interpret: During the first semester you were asked to analyze and interpret linear, quadratic and absolute value functions. Discuss how you could interpret various features of the function given various representations; table, graph, equations. Features: Line of Vertex xScale Maximum Transformations Domain Symmetry intercept(s), factor / / & y-intercept dilation Minimum Range Include a discussion of the similarities and differences of the functions: 𝑓(𝑥) = 2(𝑥 + 3) − 5 𝑔(𝑥) = 2(𝑥 + 3)2 − 5 ℎ(𝑥) = 2|𝑥 + 3| − 5 𝑗(𝑥) = |2(𝑥 + 3)2 − 5| Solving: What does it mean to solve an equation? During the first semester we studied various strategies for representing and determining solutions to equations – Linear, Quadratic, Piecewise and Absolute value. Discuss how the type and number of solutions can be determined by the various representations; table, graph, equations. Demonstrate your understanding of when and how to use each of the various solution strategies. Some terms / concepts you should include: Fundamental Nature of roots Most Factoring Quadratic Completing Theorem of efficient Formula the square / Complex – Rational Algebra / method square root Complex – Irrational number of Complex - Imaginary solutions Modeling: During the first semester we modeled linear and quadratic functions numerically, graphically and algebraically with different forms (explicit & recursive). We modeled quadratic situations; fixed perimeter rectangles & maximizing profit, and we modeled piecewise situations; traveling to and from school & draining and refilling a pool. Describe a situation for each type of function – linear, quadratic, piecewise, create the model – table, graph, equation, which could be used to model your situation then ask and answer pertinent questions.