In this unit we will learn how to graph inequalities in one and two variables and explore the region on the graph that represents the solutions to the inequality. We will learn to solve systems of two or more inequalities by graphing and locating the region on the graph that represents the solutions all the inequalities have in common. We will apply our work with systems of linear inequalities to solve linear programming problems that involve maximizing or minimizing an outcome.
Unit 2 Functions
The concept of function may be the single most important concept spanning all branches of mathematics. We will learn how to recognize when a relationship is a function and to evaluate a function for a given input. We will work with functions represented in various ways. We will recognize and interpret key features of functions represented with graphs, tables, and equations. We will relate these features to what is occurring in mathematical and real world situations. The key features include: intercepts; intervals where the function is increasing or decreasing; when the value of the function is positive or negative; relative maximums and minimums; symmetries; domain (input) and range (output); inverse relationships; and rate of change.
Unit 3 Exponential Functions
Exponential functions occur frequently in real world situations. They are used to model the growth of human and animal populations, chemical processes such as radioactive decay, and financial applications such as the compound growth of the value of an investment. Students learn about exponential functions by comparing the situations and equations for exponential functions to those for linear functions. Students recognize, use, and create tables, graphs and situations modeling exponential growth and decay. Students are able to evaluate exponential functions with rational number inputs and to relate the meaning of a rational exponent to the context of the situation. Students use tables and graphs to solve exponential equations and translate between representations.
Unit 4 Modeling with Quadratic Functions
Students use various forms of quadratic equations to graph parabolas with a focus on using the line of symmetry and the vertex. Though students will be working on converting between different forms of equations for parabolas (multiplying binomials, completing the square, and factoring), the focus is on extending their understanding from Unit 2 and recognizing the advantages of determining the location of the vertex when graphing a parabola. Students analyze graphs of quadratic functions, use graphs and tables to solve real-world situations, and translate between representations.
Unit 5 Solving Quadratic Equations
Students solve quadratic equations by factoring, finding square roots, completing the square, and by using the quadratic formula. Students determine the number of rational, real, and non-real solutions by factoring or solving the equation and also by using the graph. Students understand that the quadratic formula can be found by completing the square and use the symmetry in the graph of a parabola to identify how the x-coordinate for the vertex can be seen in the quadratic formula.
Unit 6 Polynomial Functions
Students extend earlier work with expressions to adding, subtracting, and multiplying polynomials. Students graph real-world situations that can be modeled with polynomial functions and analyze the graphs of polynomial functions. Students solve polynomial equations graphically, by using tables or by finding rational roots algebraically. Students will translate between representations of polynomial functions.
Unit 7 Root Functions and Radical Equations
Students graph square root functions and analyze the graph to identify its key features. Students evaluate and simplify radical expressions. Students solve equations with radical expressions and identify possible extraneous solutions. Students translate between representations.
Unit 8 Absolute Value Functions
Students graph real-world situations that can be modeled with absolute value functions and analyze the graphs of absolute value functions. Students solve absolute value equations and inequalities involving linear expressions in two variables by graphing, using tables and solving related equations. Students translate between representations.