Polynomial End Behavior

Front

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

Back

As x approaches positive or negative infinity, the polynomial approaches positive infinity.

Front

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

Back

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

Front

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

Back

As x approaches positive or negative infinity, the polynomial approaches negative infinity.

Front

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

Back

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

Front

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

Back

The degree is the highest power of x in the polynomial. If the ends of the graph go in the same direction, the degree is even; if they go in opposite directions, the degree is odd.

Front

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

Back

If the leading coefficient is positive, the polynomial will rise to positive infinity as x approaches positive infinity.

Front

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

Back

If the leading coefficient is negative, the polynomial will fall to negative infinity as x approaches positive infinity.

Front

What is the significance of the degree of a polynomial?

Back

The degree determines the number of turning points and the end behavior of the polynomial.

Front

What is a turning point in a polynomial graph?

Back

A turning point is where the graph changes direction, indicating a local maximum or minimum.

Front

How can you identify the leading coefficient from a polynomial equation?

Back

The leading coefficient is the coefficient of the term with the highest degree.