Polynomials - End Behavior and Graphs

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (or indeterminates) raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication.

Front

What is the degree of a polynomial?

Back

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

Front

What is the leading coefficient of a polynomial?

Back

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

Front

How does the degree of a polynomial affect its end behavior?

Back

The end behavior of a polynomial is determined by its degree and leading coefficient. For even degrees, the ends of the graph will either both go up or both go down. For odd degrees, one end will go up and the other will go down.

Front

Describe the end behavior of a polynomial with an even degree and a positive leading coefficient.

Back

As x → ∞, y → ∞ and as x → -∞, y → ∞.

Front

Describe the end behavior of a polynomial with an even degree and a negative leading coefficient.

Back

As x → ∞, y → -∞ and as x → -∞, y → -∞.

Front

Describe the end behavior of a polynomial with an odd degree and a positive leading coefficient.

Back

As x → ∞, y → ∞ and as x → -∞, y → -∞.

Front

Describe the end behavior of a polynomial with an odd degree and a negative leading coefficient.

Back

As x → ∞, y → -∞ and as x → -∞, y → ∞.

Front

What is the degree of the polynomial 3y^2 + y^4 + 4?

Back

The degree is 4.

Front

What is the leading coefficient of the polynomial 2x^3 - 5x^2 + 4?

Back

The leading coefficient is 2.