Advanced Algebra
The following learning targets represent the major concepts studied and assessed in this course.
Unit 1
Linear Functions and Absolute Values and Function Properties
- Write and graph linear equations in slope intercept form (y = ax + b) and interpret slope and y-intercept in context (including horizontal and vertical lines).
- Solve linear and absolute value equations using algebraic manipulation.
- Graph and translate absolute value functions using y = k + f(x − h).
- Combine functions and constants to create new functions using addition, subtraction, multiplication.
- Evaluate combinations of functions for given input values.
- Given two functions, compose new functions by inputting one into the other.
- Evaluate a composition of functions for given input values.
- Given a function, write the inverse.
- Determine if two functions are inverses algebraically using composition of functions.
- Graph the inverse of a function and describe its relationship to the original function.
Unit 2
Quadratics
- Graph quadratic functions in vertex, intercept and general forms.
- Find the vertex and axis of symmetry from the equation of a quadratic.
- Identify the x-intercepts of a quadratic written in intercept form.
- Rewrite an equation from vertex or intercept form to general form.
- Understand why setting a quadratic equal to 0 allows solving because of the Zero Product Property.
- Connect solving quadratics in factored form with graphing a quadratic and finding the x-intercepts.
- Solve quadratic equations with real solutions using the quadratic formula.
- Understand what the imaginary number is, why it is needed, and how to simplify expressions using it.
- Simplify square roots of negative numbers using i.
- Solve quadratic equations with imaginary solutions and identify conjugate pairs.
Unit 3
Polynomial Functions
- Identify the degree and leading coefficient of a polynomial.
- Determine end behavior of a polynomial function.
- Graph polynomial functions using intercepts, multiplicity, and end behavior.
- Identify turning points and describe intervals of increase and decrease.
- Write polynomial equations from graphs.
- Apply the Fundamental Theorem of Algebra to determine the number of zeros.
Unit 4
Polynomial Operations and Equations
- Add, subtract, and multiply polynomials.
- Factor polynomials using common factors, grouping, and special products.
- Divide polynomials using long division and synthetic division.
- Use the Remainder Theorem and Factor Theorem.
- Solve polynomial equations and identify multiplicity of roots.
Unit 5
Rational Expressions and Functions
- Simplify rational expressions.
- Perform operations with rational expressions.
- Determine restrictions on the domain.
- Solve rational equations and identify extraneous solutions.
- Graph rational functions, identifying intercepts, asymptotes, and holes.
Unit 6
Radical and Exponential Functions
- Simplify and perform operations with radicals.
- Solve radical equations and check for extraneous solutions.
- Rewrite expressions using rational exponents.
- Graph exponential functions and describe transformations.
- Solve exponential equations algebraically and graphically.
- Apply exponential functions to real-world contexts.