Graphing Polynomials Flashcard

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

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.

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

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.

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

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

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

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.

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

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