Graphing polynomial functions

Front

What are the zeros of the function f(x)=(x+4)(x-3)(x-2)?

Back

The zeros are x=-4, x=3, x=2.

Front

What does it mean when a function crosses the x-axis?

Back

It means that the function has zeros at those points.

Front

How do you express a polynomial function in factored form if its zeros are 2, 3, and -1?

Back

The factored form is (x-2)(x-3)(x+1).

Front

What are 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 zeros of a polynomial function?

Back

The zeros indicate the x-values where the function equals zero, or where it intersects the x-axis.

Front

What is the general form of a polynomial function?

Back

A polynomial function is generally expressed as f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n ≠ 0.

Front

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

Back

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

Front

What is the factored form of a polynomial with zeros at -2, 0, and 5?

Back

The factored form is f(x) = (x + 2)(x)(x - 5).

Front

How can you find the zeros of a polynomial function graphically?

Back

By identifying the points where the graph intersects the x-axis.

Front

What is the multiplicity of a zero?

Back

The multiplicity of a zero refers to the number of times a particular zero is repeated in the factored form of the polynomial.