Polynomial-monomial or the sum of monomials
Polynomial Function-a polynomial with the value x
Standard Form of a polynomial -
Naming By Degree and Terms:
Monomial- polynomial with 1 term
Binomial- polynomial with 2 terms
Trinomial- polynomial with 3 terms
***Polynomials with 4 or more terms do not have specific names
Degree of a Polynomial- the highest exponent among the monomial terms
Turning Point:the point(s) where a graph changes direction
End behavior: the directions of the graph to the far left and to the far right
Examples:
Finite Differences: When you are given a set of polynomial function outputs, the x-values are the ordered inputs that differ by a constant. Analyzing the differences of consecutive y-values, one can find out the least-degree polynomial function for the set of values. For instance, if the first differences are constant, the function is linear, but if the second differences are constant, then the function is a quadratic.
Example:
Extra Practice
Write each polynomial in function in standard form, classify it by degree, and determine the end behavior of its graph.
1. 12-x4
2. y=10-3x3+3x2+x4
3. A polynomial function p(x) has degree n. If n is even, is the number of turning points of the graph even or odd? What can you say about the number of turning points if n is odd?
