Polynomial and Rational Functions (39 topics)

Quadratic Functions (9 topics)

• Finding the zeros of a quadratic function given its equation
• Using a graphing calculator to find the zeros of a quadratic function
• Writing a quadratic function given its zeros
• Finding the x-intercepts and the vertex of a parabola
• Using a graphing calculator to find the x-intercept(s) and vertex of a quadratic function
• Rewriting a quadratic function to find its vertex and sketch its graph
• Finding the maximum or minimum of a quadratic function
• Word problem involving the maximum or minimum of a quadratic function
• Word problem involving optimizing area by using a quadratic function

Polynomial Functions (6 topics)

• Finding zeros and their multiplicities given a polynomial function written in factored form
• Finding a polynomial of a given degree with given zeros - Real zeros
• Finding x- and y-intercepts given a polynomial function
• Determining the end behavior of the graph of a polynomial function
• Determining end behavior and intercepts to graph a polynomial function
• Using a graphing calculator to find local extrema of a polynomial function

Division of Polynomials; Remainder and Factor Theorems (4 topics)

• Polynomial long division - Problem type 3
• Synthetic division
• Using the remainder theorem to evaluate a polynomial
• The Factor Theorem

Real Zeros of Polynomial Functions (3 topics)

• Using a given zero to write a polynomial as a product of linear factors - Real zeros
• Using the rational zeros theorem to find all zeros of a polynomial - Irrational zeros
• Using a graphing calculator to find zeros of a polynomial function

Complex Zeros of Polynomials Functions (4 topics)

• Multiplying expressions involving complex conjugates
• Finding a polynomial of a given degree with given zeros - Complex zeros
• Using a given zero to write a polynomial as a product of linear factors - Complex zeros
• Using the rational zeros theorem to find all zeros of a polynomial - Complex zeros

Rational Functions (10 topics)

• Finding the intercepts, asymptotes, domain, and range from the graph of a rational function
• Finding the asymptotes of a rational function - Constant over linear
• Finding the asymptotes of a rational function - Linear over linear
• Finding horizontal and vertical asymptotes of a rational function - Quadratic numerator or denominator
• Finding the asymptotes of a rational function - Quadratic over linear
• Graphing a rational function - Constant over linear
• Graphing a rational function - Linear over linear
• Transforming the graph of a rational function
• Graphing a rational function - Quadratic over linear
• Graphing rational functions with holes

Polynomial and Rational Inequalities (3 topics)

• Solving a quadratic inequality
• Solving a polynomial inequality - Problem type 2
• Solving a polynomial inequality - Problem type 4