End Behavior

Front

What is end behavior in a polynomial function?

Back

End behavior describes the behavior of the graph of a polynomial function as the input values (x) approach positive or negative infinity.

Front

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

Back

The end behavior can be determined by the leading term of the polynomial, specifically the leading coefficient and the degree of the polynomial.

Front

What does it mean if a polynomial has a positive leading coefficient?

Back

If a polynomial has a positive leading coefficient, the graph will rise to the right as x approaches positive infinity.

Front

What does it mean if a polynomial has a negative leading coefficient?

Back

If a polynomial has a negative leading coefficient, the graph will fall to the right as x approaches positive infinity.

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

What is the significance of the degree of a polynomial in determining end behavior?

Back

The degree of a polynomial determines whether the ends of the graph will rise or fall. Even degrees lead to both ends behaving the same, while odd degrees lead to opposite behaviors.

Front

What happens to the graph of a polynomial function as x approaches positive infinity if the degree is even and the leading coefficient is positive?

Back

The graph will rise to positive infinity on both ends.

Front

What happens to the graph of a polynomial function as x approaches negative infinity if the degree is even and the leading coefficient is negative?

Back

The graph will fall to negative infinity on both ends.

Front

What are zeros of a polynomial function?

Back

Zeros are the values of x for which the polynomial function equals zero; they are the x-intercepts of the graph.

Front

How can you find the zeros of a quadratic function?

Back

You can find the zeros of a quadratic function by factoring, using the quadratic formula, or completing the square.