Graphing polynomials

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

Which root has the highest multiplicity in the function y=(8-x)^2(x+1)(x-2)^3(x-1)?

Back

The root with the highest multiplicity is x=2.

Front

If the graph of a function crosses the x-axis, what does that indicate about the multiplicity of that zero?

Back

It indicates that the multiplicity of that zero is odd.

Front

How many solutions does the polynomial y=(8-x)^2(x+1)(x-2)^3(x-1) have?

Back

The polynomial has 4 solutions.

Front

What is the degree of the polynomial function f(x)=(x+4)(x-3)(x-2)?

Back

The degree of the function is 3.

Front

Define a polynomial function.

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in the polynomial.

Front

What does the degree of a polynomial indicate about its graph?

Back

The degree of a polynomial indicates the maximum number of x-intercepts (real roots) and the end behavior of the graph.

Front

What is the difference between even and odd multiplicity of a zero?

Back

Even multiplicity means the graph touches the x-axis at that zero, while odd multiplicity means the graph crosses the x-axis.

Front

How can you determine the number of turning points in a polynomial graph?

Back

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