2.2 Practice - Graphing Higher Order Polynomials

Front

What is the end behavior of a polynomial function with a leading coefficient that is negative and an even degree?

Back

The end behavior will be down/down.

Front

What is the end behavior of a polynomial function with a leading coefficient that is positive and an odd degree?

Back

The end behavior will be up/down.

Front

What does it mean for a graph to 'bounce' at a root?

Back

A graph 'bounces' at a root when the root has an even multiplicity.

Front

What does it mean for a graph to 'cross' at a root?

Back

A graph 'crosses' at a root when the root has an odd multiplicity.

Front

Identify the degree and leading coefficient of the polynomial: g(x) = -2x^6 + 2x^5 - 12x - 6.

Back

Degree: 6, Leading Coefficient: Negative.

Front

Back

Front

What is the factored form of a polynomial?

Back

A polynomial expressed as a product of its linear factors.

Front

What is the significance of the leading coefficient in determining the end behavior of a polynomial?

Back

The sign of the leading coefficient determines whether the ends of the graph go up or down.

Front

How do you determine the number of real roots of a polynomial?

Back

By analyzing the degree and using the Rational Root Theorem.

Front

What is the relationship between the degree of a polynomial and the maximum number of turning points?

Back

The maximum number of turning points is one less than the degree of the polynomial.