Exploring Polynomial End Behavior

This video tutorial discusses the end behavior of polynomials, focusing on how they behave as x becomes very large or very negative. It covers quadratic, third, fourth, and fifth degree polynomials, explaining how the leading coefficient and the degree of the polynomial affect the graph's end behavior. The video highlights the similarities between even and odd degree polynomials and their respective end behaviors, emphasizing the importance of the leading term in determining the graph's behavior at extreme values of x.

What happens to a quadratic polynomial when the coefficient 'a' is greater than 0?

• It oscillates.

• It remains constant.

• It opens upward.

• It opens downward.

For a third-degree polynomial with a positive 'a', what is the end behavior as x becomes very large?

• It becomes very negative.

• It oscillates.

• It remains constant.

• It becomes very positive.

What is the end behavior of a third-degree polynomial with a negative 'a' as x becomes very negative?

• It becomes very negative.

• It oscillates.

• It becomes very positive.

• It remains constant.

How does the end behavior of a fourth-degree polynomial compare to a second-degree polynomial when 'a' is positive?

• It remains constant.

• It is similar.

• It oscillates.

• It is very different.

What happens to a fourth-degree polynomial with a negative 'a' as x becomes very positive?

• It oscillates.

• It becomes very negative.

• It remains constant.

• It becomes very positive.

What is the end behavior of a polynomial with an even highest degree term when 'a' is positive?

• It remains constant.

• It becomes very negative.

• It becomes very positive.

• It oscillates.

For a polynomial with an odd highest degree term and a positive 'a', what is the end behavior as x becomes very negative?

• It becomes very negative.

• It remains constant.

• It becomes very positive.

• It oscillates.

What is the end behavior of a fifth-degree polynomial with a positive 'a' as x becomes very large?

• It becomes very negative.

• It remains constant.

• It becomes very positive.

• It oscillates.

How does the end behavior of an odd degree polynomial compare to a third-degree polynomial?

• It oscillates.

• It is very different.

• It is similar.

• It remains constant.

What is the general end behavior of an even degree polynomial?

• Similar to a second-degree polynomial.

• It oscillates.

• Similar to a third-degree polynomial.

• It remains constant.