Graphs of Polynomials Review

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It determines the end behavior of the graph.

Front

How does the degree of a polynomial affect its graph?

Back

The degree of a polynomial indicates the number of roots and the general shape of the graph. Odd degree polynomials have opposite end behaviors, while even degree polynomials have the same end behavior.

Front

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

Back

An odd degree polynomial has at least one root and its graph will cross the x-axis at least once. The ends of the graph will go in opposite directions.

Front

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

Back

An even degree polynomial has roots that can be repeated and its graph will not cross the x-axis an odd number of times. The ends of the graph will go in the same direction.

Front

What is multiplicity in relation to polynomial roots?

Back

Multiplicity refers to the number of times a particular root appears in a polynomial. A root with an even multiplicity will touch the x-axis, while a root with an odd multiplicity will cross it.

Front

How can you determine the end behavior of a polynomial function?

Back

The end behavior of a polynomial function can be determined by its leading coefficient and degree. For example, a positive leading coefficient with an even degree will rise on both ends.

Front

What is the significance of the x-intercepts of a polynomial graph?

Back

The x-intercepts, or roots, of a polynomial graph indicate the values of x for which the polynomial equals zero. They are crucial for understanding the graph's behavior.

Front

What is the relationship between the degree of a polynomial and the number of roots it can have?

Back

A polynomial of degree n can have up to n roots, counting multiplicities.

Front

What does a positive leading coefficient indicate about the graph of a polynomial?

Back

A positive leading coefficient indicates that the graph will rise to the right. If the degree is even, it will also rise to the left.

Front

What does a negative leading coefficient indicate about the graph of a polynomial?

Back

A negative leading coefficient indicates that the graph will fall to the right. If the degree is even, it will also fall to the left.