End Behavior of Polynomials

Front

What is the end behavior of a polynomial?

Back

The end behavior of a polynomial describes how the graph behaves as x approaches positive or negative infinity.

Front

What determines the end behavior of a polynomial?

Back

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

Front

What is a leading coefficient?

Back

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

Front

How does the sign of the leading coefficient affect end behavior?

Back

If the leading coefficient is positive, the graph rises to the right; if negative, it falls to the right.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest exponent of the variable in the polynomial.

Front

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

Back

The degree is 3.

Front

What does a polynomial of degree 2 look like in terms of end behavior?

Back

A polynomial of degree 2 (quadratic) opens upwards if the leading coefficient is positive and downwards if negative.

Front

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

Back

The end behavior is down to the left and up to the right.

Front

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

Back

The end behavior is down to the left and down to the right.

Front

How can you determine the end behavior from a polynomial equation?

Back

Identify the leading term and analyze its degree and leading coefficient.