Algebra 2

In this unit, students will apply transformations to functions. They use equations to transform functions and to model situations involving swimming, roller coasters, and mental health. They also revisit key features of functions, including domain and range. 

In this unit, students will extend what they learned in Algebra 1 to rewrite quadratic functions in different forms, determine their key features, and solve quadratic equations. Students will discover the imaginary unit i and write equivalent expressions involving adding, subtracting, and multiplying complex numbers.

In this unit, students will extend their knowledge of linear and quadratic functions to polynomial functions of higher degree. They will describe key features of polynomials from their graphs and equations, rewriting functions in different forms to support their thinking. They will explore two new key features: end behavior and multiplicities of zeros. Students will also sketch graphs, write equations, and solve for all real and non-real zeros of polynomials.

In this unit, students will graph rational functions and analyze them to determine some of their key features, including asymptotes and holes. Students will also write and solve rational equations and model real-world situations using rational functions.

In this unit, students will extend their understanding of inverse operations to write and analyze square-root and cube-root functions. They will explore the properties of root functions and of inverse functions more generally. Then they will graph square and cube root functions by hand and using technology. They will also write and solve radical equations and inequalities in context, then will explore a real-world situation that can be modeled by radical equations.

In this unit, students will extend their understanding of exponential functions from Algebra 1. They will write and interpret exponential functions in context, including situations that compound continuously. They will explore how to use logarithms to solve exponential equations. They will also describe connections between the graphs, tables, key features, and equations of exponential functions and their logarithmic inverses. 

In this unit, students will explore how circular motion can give rise to periodic functions. They will build on their understanding of trigonometric ratios to discover relationships between angles and coordinates on the unit circle, then use these insights to prove and apply the Pythagorean identity. Then they will define trigonometric functions, using angles measured in radians as inputs, exploring the graphs and key features of these functions. Finally, students will learn about transformations of these functions and use them to model periodic situations in the real world.