Polynomial Characteristics Check

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

How do you determine the x-intercepts of a polynomial function?

Back

To find the x-intercepts, set the polynomial equal to zero and solve for x.

Front

What does it mean if a polynomial has an even degree?

Back

A polynomial with an even degree will have the same end behavior on both sides of the graph (either both ends up or both ends down).

Front

What is a leading coefficient?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

How does the leading coefficient affect the graph of a polynomial?

Back

The sign of the leading coefficient determines the end behavior of the polynomial's graph.

Front

What is the significance of x-intercepts in a polynomial function?

Back

X-intercepts indicate the points where the graph of the polynomial crosses the x-axis.

Front

What does it mean for a polynomial to be increasing?

Back

A polynomial is increasing on an interval if the function values rise as x values increase within that interval.

Front

What is the relationship between the degree of a polynomial and the number of x-intercepts?

Back

A polynomial of degree n can have at most n x-intercepts.

Front

What is the difference between odd and even degree polynomials?

Back

Odd degree polynomials have opposite end behaviors, while even degree polynomials have the same end behavior.

Front

How can you identify the intervals where a polynomial is increasing or decreasing?

Back

By analyzing the first derivative of the polynomial, you can find critical points and determine intervals of increase or decrease.