Honors Pre-Calculus A, 1st Hour, Winter 2015: Polynomial Functions

Polynomial functions can be defined as:

when a to the subscript n is non negative, or equals 0 or an integer, but cannot be a fraction. Therefore, polynomial functions must always have the domain of all real numbers because the graphs are continuous and never ending. The coefficients of the terms must also be real numbers.

For example,

are all polynomial functions because they can be solved for all real numbers.

On the other hand, x+5/x+3 is not a polynomial function because it is undefined when x=3, meaning that the denominator is equal to zero. Because the graph is not one continuous line, the function is not a polynomial.

Likewise, square root of x or the absolute value of x are not polynomial functions.

graph portrays the square root of x.

Degrees of Polynomials

If the highest degree of x is o, then the equation is considered constant.
ex. f(x)=2

When the highest degree (or power) of x is a first degree, that polynomial is considered Linear.
ex.

A Quadratic equation is one in which the highest degree of x is to the second power.
ex

A Cubic polynomial has a third degree as its highest power of x.
ex

Quadratics
The standard form of a quadratic equation for a parabola is

In this form, the point (h,k) marks the vertex of the graph of the equation.

Standard form is found by completing the square

For Example, when given