Graphs of polynomials

The  exercise appears under the Algebra II Math Mission. This exercise emphasizes the connection between the algebraic "zero" of a function and the geometric "x-intercept."

Types of Problems
There are two types of problems in this exercise:


 * 1) Analyze the polynomials and some of its forms: This problem provides a polynomial and asks a set of questions about it. Generally, the student is expected to know which form of a polynomial is useful for different questions about the polynomial.Grofpo1.png
 * 2) Match the graphs: This problem provides a collection of functions and a collection of graphs. The student is asked to match each function with it's graph using a provided chart.Grofpo2.png

Strategies
Knowledge of graphing and some of the polynomial theorems are encouraged to ensure success on this exercise.
 * 1) The factored form of a polynomial is best for determining it's zeroes.
 * 2) The fully expanded form of a polynomial is best to determine it's end behavior.
 * 3) The end behavior of a polynomial is generally determined by it's leading terms coefficient and the parity of it's degree.
 * 4) A zero of an equation is an x-intercept of it's graph.
 * 5) A polynomial with an x-intercept of (r,0) will have a factor of (x-r) and the remainder when divided by (x-r) will be zero.

Real-life Applications

 * 1) Graphing is an important concept in calculus and beyond that can be made easier with advanced techniques for graphing. Recognizing the connection between a factored polynomials and it's zeroes helps this application.