Zeros & Multiplicity (Alg 2 Friendly)

Front

What does it mean if the graph of a function crosses the x-axis?

Back

The zero has an odd multiplicity (1, 3, etc.).

Front

How does a zero with multiplicity 2 affect the graph?

Back

The graph will bounce off the x-axis at that zero.

Front

Back

The zeros are 0, 6, and -5.

Front

Back

The roots are -2 and 7 with multiplicity 3.

Front

Define 'zero' in the context of polynomial functions.

Back

A zero is a value of x that makes the function equal to zero.

Front

What is multiplicity in relation to zeros?

Back

Multiplicity refers to the number of times a particular zero occurs.

Front

If a zero has an even multiplicity, how does the graph behave at that zero?

Back

The graph touches the x-axis and does not cross it.

Front

What is the significance of a zero with multiplicity 1?

Back

The graph crosses the x-axis at that zero.

Front

How can you determine the multiplicity of a zero from a polynomial's factors?

Back

The multiplicity is equal to the exponent of the factor corresponding to that zero.

Front

What is the relationship between the degree of a polynomial and its zeros?

Back

The degree of a polynomial is equal to the total number of its zeros, counting multiplicities.