End Behavior & Zeros of Polynomials

Front

What are the zeros of the polynomial function y = x(x - 6)(x + 5)?

Back

0, 6, -5

Front

What determines the end behavior of a polynomial function?

Back

The degree and the sign of the leading coefficient.

Front

Identify the degree of the polynomial f(x)= x^3(x + 3)^2(x – 5).

Back

Degree: 6

Front

Determine the end behavior of the graph of f(x) = -7x^3 + 2x - 1.

Back

As x → ∞, f(x) → -∞; As x → -∞, f(x) → ∞.

Front

What is the term that affects the end behavior of a polynomial?

Back

Leading Term

Front

What is the degree of a polynomial?

Back

The highest power of the variable in the polynomial.

Front

How do you find the zeros of a polynomial?

Back

Set the polynomial equal to zero and solve for the variable.

Front

What is the leading coefficient of a polynomial?

Back

The coefficient of the term with the highest degree.

Front

What is the end behavior of a polynomial with an even degree and a positive leading coefficient?

Back

As x → ∞, f(x) → ∞; As x → -∞, f(x) → ∞.

Front

What is the end behavior of a polynomial with an odd degree and a negative leading coefficient?

Back

As x → ∞, f(x) → -∞; As x → -∞, f(x) → ∞.