Graphs of Polynomials Review

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 if a polynomial is of even or odd degree?

Back

A polynomial is of even degree if the highest power of the variable is even (e.g., 0, 2, 4). It is of odd degree if the highest power is odd (e.g., 1, 3, 5).

Front

What does the leading coefficient of a polynomial indicate?

Back

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

Front

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

Back

As x approaches positive infinity, the polynomial approaches positive infinity; as x approaches negative infinity, the polynomial approaches negative infinity.

Front

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

Back

As x approaches positive infinity, the polynomial approaches negative infinity; as x approaches negative infinity, the polynomial approaches positive infinity.

Front

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

Back

As x approaches both positive and negative infinity, the polynomial approaches positive infinity.

Front

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

Back

As x approaches both positive and negative infinity, the polynomial approaches negative infinity.

Front

How can you identify the degree of a polynomial from its graph?

Back

The degree can often be identified by the number of turning points in the graph. A polynomial of degree n can have at most n-1 turning points.

Front

What is a turning point in the context of polynomial graphs?

Back

A turning point is a point on the graph where the direction of the graph changes from increasing to decreasing or vice versa.

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.