Graphing Polynomials Flashcard

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its factors, which can include linear factors and constants.

Front

What does the multiplicity of a root indicate in a polynomial graph?

Back

Multiplicity indicates how many times a particular root appears. A root with odd multiplicity crosses the x-axis, while a root with even multiplicity touches the x-axis.

Front

How do you determine the number of zeros of a polynomial function?

Back

The number of zeros of a polynomial function is determined by its degree, which is the highest power of the variable in the polynomial.

Front

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

Back

The leading coefficient determines the end behavior of the polynomial graph. A positive leading coefficient means the graph rises to the right, while a negative leading coefficient means it falls to the right.

Front

What is an even function?

Back

An even function is symmetric about the y-axis, meaning f(x) = f(-x) for all x in the domain.

Front

What is an odd function?

Back

An odd function is symmetric about the origin, meaning f(-x) = -f(x) for all x in the domain.

Front

How can you identify the degree of a polynomial?

Back

The degree of a polynomial is identified by the highest exponent of the variable in the polynomial expression.

Front

What does it mean for a polynomial to have an even degree?

Back

A polynomial with an even degree has a graph that approaches the same direction (either both up or both down) as x approaches positive and negative infinity.

Front

What does it mean for a polynomial to have an odd degree?

Back

A polynomial with an odd degree has a graph that approaches opposite directions as x approaches positive and negative infinity.

Front

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

Back

The x-intercepts of a polynomial function are found by setting the polynomial equal to zero and solving for x.