Graphing Polynomials

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x for which the polynomial equals zero.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros, set the polynomial equal to zero and solve for x.

Front

What does it mean if a polynomial has an odd multiplicity at a zero?

Back

If a polynomial has an odd multiplicity at a zero, the graph crosses the x-axis at that zero.

Front

What does it mean if a polynomial has an even multiplicity at a zero?

Back

If a polynomial has an even multiplicity at a zero, the graph touches the x-axis but does not cross it.

Front

How many zeros can a polynomial of degree n have?

Back

A polynomial of degree n can have up to n zeros.

Front

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

Back

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

Front

What is multiplicity in relation to polynomial zeros?

Back

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

Front

Given the polynomial P(x) = 3x^4 + 4x - 8, how many zeros does it have?

Back

It has 4 zeros.

Front

Identify the zeros of the polynomial y = 3(x + 4)(x + 1)(x - 3).

Back

The zeros are -4, -1, and 3.

Front

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

Back

The leading coefficient affects the end behavior of the graph of the polynomial.