Polynomial Graphs Key Features

Front

What does the leading coefficient of a polynomial determine?

Back

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

Front

What is the relationship between x-intercepts and polynomial factors?

Back

Each x-intercept (a,b) corresponds to a factor of the form (x-a) in the polynomial.

Front

What does a positive leading coefficient indicate about the graph of a polynomial?

Back

If the leading coefficient is positive, the graph rises to the right.

Front

What does a negative leading coefficient indicate about the graph of a polynomial?

Back

If the leading coefficient is negative, the graph falls to the right.

Front

How can you determine the degree of a polynomial from its graph?

Back

The degree of a polynomial is the highest power of x in the polynomial expression, which can be inferred from the number of turns in the graph.

Front

What does an even degree polynomial graph look like?

Back

An even degree polynomial graph has both ends going in the same direction (either up or down).

Front

What does an odd degree polynomial graph look like?

Back

An odd degree polynomial graph has ends going in opposite directions (one up and one down).

Front

What is the significance of the constant term in a polynomial?

Back

The constant term represents the y-intercept of the polynomial graph.

Front

How does the number of x-intercepts relate to the degree of the polynomial?

Back

A polynomial of degree n can have at most n x-intercepts.

Front

What is the effect of a negative constant term on the graph of a polynomial?

Back

A negative constant term means the graph will cross the y-axis below the origin.