Graphing Polynomials

Front

What is a polynomial?

Back

Front

What does the degree of a polynomial represent?

Back

Front

What is a leading coefficient?

Back

Front

How do you determine if a polynomial is increasing or decreasing?

Back

A polynomial is increasing on an interval if its derivative is positive on that interval, and decreasing if its derivative is negative.

Front

What is the significance of the leading coefficient's sign?

Back

The sign of the leading coefficient determines the end behavior of the polynomial. If it is positive and the degree is even, the graph rises on both ends; if it is negative, it falls on both ends.

Front

What is an even function?

Back

Front

What is an odd function?

Back

Front

What is the interval of increase for a polynomial?

Back

The interval of increase for a polynomial is the range of x-values where the function's output is increasing. This can be found by analyzing the derivative.

Front

What is the interval of decrease for a polynomial?

Back

The interval of decrease for a polynomial is the range of x-values where the function's output is decreasing. This can be determined by finding where the derivative is negative.

Front

How do you find the x-intercepts of a polynomial?

Back

To find the x-intercepts of a polynomial, set the polynomial equal to zero and solve for x. The solutions are the x-intercepts.