Polynomial Graphs

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x for which the polynomial equals zero.

Front

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

Back

It means the ends of the graph of the polynomial will rise on both sides.

Front

What is the leading coefficient of the polynomial f(x) = -8x^4 + 6x^3 + 11?

Back

The leading coefficient is -8.

Front

What is the range of the polynomial f(x) = -8x^4 + 6x^3 + 11?

Back

The range is y ≤ 0.

Front

What does multiplicity mean in the context of polynomial roots?

Back

Multiplicity refers to the number of times a particular root appears in the factorization of a polynomial.

Front

How do you find the zeros of a polynomial graphically?

Back

You find the zeros by identifying the x-intercepts of the graph.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial's graph.

Front

What does it mean if a polynomial has an odd degree?

Back

If a polynomial has an odd degree, the ends of the graph will go in opposite directions.

Front

How can you determine the number of turning points in a polynomial graph?

Back

The maximum number of turning points is one less than the degree of the polynomial.

Front

What is the relationship between the degree of a polynomial and the number of zeros it can have?

Back

A polynomial of degree n can have up to n zeros.