Polynomial Graphs Key Features

Front

What is the degree of a polynomial if its graph has both ends going up?

Back

The degree of the polynomial is even.

Front

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

Back

The graph rises to the right.

Front

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

Back

The graph falls to the right.

Front

If a polynomial has an x-intercept at (3,0), what is the corresponding factor?

Back

The factor is (x-3).

Front

If a polynomial has an x-intercept at (-5,0), what is the corresponding factor?

Back

The factor is (x+5).

Front

What does the constant term of a polynomial represent in its graph?

Back

The y-intercept of the graph.

Front

If the constant term of a polynomial is positive, where does the graph intersect the y-axis?

Back

The graph intersects the y-axis above the origin.

Front

If the constant term of a polynomial is negative, where does the graph intersect the y-axis?

Back

The graph intersects the y-axis below the origin.

Front

What is the significance of the number of x-intercepts in a polynomial graph?

Back

It indicates the number of real roots of the polynomial.

Front

What does it mean if a polynomial has a repeated x-intercept?

Back

The corresponding factor is squared, indicating a bounce at that intercept.