Zeros & Multiplicity (Alg 2 Friendly)

Front

What is a zero of a polynomial?

Back

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

Front

How does a multiplicity of 1 affect the graph at a zero?

Back

The graph crosses the x-axis at the zero.

Front

How does a multiplicity of 2 affect the graph at a zero?

Back

The graph bounces off the x-axis at the zero.

Front

How does a multiplicity of 3 affect the graph at a zero?

Back

The graph squiggles or changes direction at the zero.

Front

What are the zeros of the polynomial y = 2(x - 1)(x + 2)(x - 3)?

Back

The zeros are 1, -2, and 3.

Front

If a polynomial has a zero with multiplicity 4, how does it behave at that zero?

Back

The graph touches the x-axis and flattens out at that zero.

Front

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

Back

The degree of a polynomial indicates the maximum number of zeros it can have.

Front

What does it mean for a zero to have an even multiplicity?

Back

A zero with an even multiplicity results in the graph touching the x-axis but not crossing it.

Front

What does it mean for a zero to have an odd multiplicity?

Back

A zero with an odd multiplicity results in the graph crossing the x-axis.

Front

Given the polynomial y = (x + 1)(x - 2)^2, identify the zeros and their multiplicities.

Back

Zeros: -1 (mult. 1), 2 (mult. 2).