Polynomial Functions A function defined by an equation in the form where is a non-negative integer and the are constants.

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Presentation transcript:

Polynomial Functions A function defined by an equation in the form where is a non-negative integer and the are constants.

Graphs of Polynomial Functions Continuous Smooooooooth Leading Coefficient Test Real Zeros of the function

Linear Quadratic Cubic General Shapes of Functions

QuarticQuintic General Shapes of Functions

LinearCubic Quintic

General Shapes of Functions QuadraticQuartic

Leading Coefficient Test Remember, when we talk about increasing or decreasing, rising or falling, we always are going from left to right! Describes end behavior Positive leading coefficients always end up rising Negative leading coefficients always end up falling Odd degrees start and end in opposite directions Even degrees start and end in the same direction

Real Zeros of Polynomial Functions If f is a polynomial function and a is a real number, then the following statements are equivalent: If f is a polynomial function and a is a real number, then the following statements are equivalent:  x=a is a zero of the function f  x=a is a solution of the polynomial f(x)=0  (x-a) is a factor of f  (a,0) is an x-intercept of the graph of f(x)

Find all real zeros of Solution:

Find the real zeros of Use your calculator to graph and find the zeros! IT’S UGLY!

Find the real zeros of Factor to find the zeros! Note: This function “bounces” off the x-axis at x=0. This means that there is a double root there

The more roots at a particular spot … The flatter the graph becomes there