Graphing Polynomials

Front

What is a polynomial?

Back

Front

What are the x-intercepts of a polynomial?

Back

The x-intercepts of a polynomial are the values of x for which the polynomial equals zero. They are the points where the graph of the polynomial crosses the x-axis.

Front

What does it mean for an x-intercept to 'bounce'?

Back

An x-intercept 'bounces' when the corresponding factor of the polynomial has an even exponent. This means the graph touches the x-axis at that point but does not cross it.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by its leading term. If the leading coefficient is positive and the degree is even, the ends of the graph rise. If the leading coefficient is negative and the degree is even, the ends fall.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It influences the direction of the graph's end behavior.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. It determines the number of x-intercepts and the general shape of the graph.

Front

What is the difference between even and odd degree polynomials?

Back

Even degree polynomials have a symmetric graph about the y-axis, while odd degree polynomials have a graph that is symmetric about the origin.

Front

How can you find the number of x-intercepts of a polynomial?

Back

The number of x-intercepts of a polynomial can be found by determining the roots of the polynomial equation. The maximum number of x-intercepts is equal to the degree of the polynomial.

Front

What is a multiplicity of a root?

Back

The multiplicity of a root refers to the number of times a particular root appears in the factorization of a polynomial. A root with an odd multiplicity will cross the x-axis, while a root with an even multiplicity will bounce.

Front

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

Back

The constant term of a polynomial is the value of the polynomial when the variable is zero. It represents the y-intercept of the graph.