Alg2 Topics

• Prepare a mathematical analysis of a problem modeled by a linear function.
• Solve linear equations.
• Understand the concept of inequalities.
• Solve, graph, and interpret linear inequalities.
• Model and solve systems of two equations or inequalities.
• Understand what is meant by a solution to a system of equations or inequalities.
• Use systems of equations or inequalities to solve real-world problems.
• Connect graphical, tabular, and algebraic representations.
• Define and identify exponential and logarithmic functions.
• Model exponential and logarithmic functions algebraically and graphically.
• Understand the relationship between exponential and logarithmic functions.
• Compare basic properties of linear and exponential functions.
• Understand the relationship between the symbolic and graphical representations for quadratic functions.
• Transform quadratic functions graphically and algebraically.
• Define quadratic equations.
• Model quadratic equations algebraically and graphically.
• Solve quadratic equations.
• Factor quadratic equations.
• Simplify expressions involving radicals.
• Solve equations involving radicals.
• Solve quadratic equations with a negative discriminant.
• Define a complex number.
• Perform arithmetic operations with complex numbers.
• Define and identify a polynomial function and the family of polynomial functions
• Model and graph situations involving polynomial functions.
• Find the zeros of polynomial functions.
• Add and subtract polynomial expressions.
• Identify and describe equations for absolute value functions, piecewise linear functions, step functions, rational functions, and logistic functions.
• Graph and write equations for absolute value functions, piecewise linear functions, step functions, rational functions, and logistic functions.
• Identify and classify discontinuity in functions.
• Differentiate between relations and functions.
• Define inverse and identity functions.
• Determine whether a function is one-to-one.
• Determine the inverses of linear, power, exponential, and rational functions.
• Transform functions.
• Define each conic section algebraically as a locus of points.
• Use transformations to generalize each equation.
• Define and identify key components such as the center, foci, vertices, covertices, major and minor axes, directrix, axis of symmetry, and asymptotes.
• Write and solve systems of linear and quadratic equations.
• Write and solve systems of linear and exponential equations.
• Model problem situations with systems of linear equations.

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