Polynomial End Behavior

Front

What is the leading coefficient of a polynomial?

Back

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

Front

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

Back

The end behavior of a polynomial function is determined by the degree of the polynomial and the sign of the leading coefficient.

Front

What is the leading coefficient of the polynomial f(x) = -3x^2 - 5x - 4?

Back

The leading coefficient is -3.

Front

What is the degree of the polynomial f(x) = -3x^2 - 5x - 4?

Back

The degree is 2.

Front

If a polynomial has a negative leading coefficient and an odd degree, what is the end behavior?

Back

As x approaches positive infinity, f(x) approaches negative infinity; as x approaches negative infinity, f(x) approaches positive infinity.

Front

If a polynomial has a positive leading coefficient and an odd degree, what is the end behavior?

Back

As x approaches positive infinity, f(x) approaches positive infinity; as x approaches negative infinity, f(x) approaches negative infinity.

Front

What is the maximum number of real zeros for a polynomial of degree n?

Back

The maximum number of real zeros for a polynomial of degree n is n.

Front

What is the maximum number of real zeros for the polynomial f(x) = 2x^4 + 19x^2 + 24?

Back

The maximum number of real zeros is 4.

Front

What is the maximum number of real zeros for the polynomial f(x) = (x+4)(x-3)(x-2)?

Back

The maximum number of real zeros is 3.

Front

What does it mean if a polynomial has an even degree and a positive leading coefficient?

Back

The end behavior will be both ends of the graph rising; as x approaches both positive and negative infinity, f(x) approaches positive infinity.