Using zeros to graph 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 three types of problems in this exercise:


 * 1) Determine the graph of the given function: This problem provides a function and several graphs. The student is asked to determine which graph displays the function.Uztgp1.png
 * 2) Determine all functions that could be the graph: This problem provides a graph and several possible functions. The student is asked to determine all of the functions that could possibly represent the graph.Uztgp2.png
 * 3) Plot the x-intercepts: This problem provides a function and a coordinate plane. The student is expected to find the zeroes of the function and plot only these, as x-intercepts, on the plane.Uztgp3.png

Strategies
Knowledge of graphing and some of the polynomial theorems are encouraged to ensure success on this exercise.
 * 1) A zero of an equation is an x-intercept of it's graph.
 * 2) 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.