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).

Front

What does it mean if the graph does not cross the x-axis?

Back

The zero has an even multiplicity (2, 4).

Front

What does the degree of a polynomial determine?

Back

The maximum number of roots.

Front

What are the zeros of the polynomial function y = x(x - 6)(x + 5)?

Back

0, 6, -5

Front

What are the roots of the function y = (x + 2)(x - 7)^3?

Back

-2, 7 with multiplicity 3.

Front

Define 'zero' in the context of polynomial functions.

Back

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

Front

What is multiplicity in relation to zeros?

Back

Multiplicity refers to the number of times a particular zero is repeated.

Front

How does the multiplicity of a zero affect the graph of a polynomial?

Back

Odd multiplicity means the graph crosses the x-axis; even multiplicity means it touches and turns around.

Front

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

Back

The maximum number of turning points is one less than the degree of the polynomial.

Front

If a polynomial has a degree of 4, what is the maximum number of zeros it can have?

Back

4 zeros.