Polynomial Graphs

Front

What is the general form of a polynomial function?

Back

A polynomial function is 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 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. Higher degree polynomials can have more complex shapes.

Front

What is a zero of a polynomial function?

Back

A zero of a polynomial function is a value of x for which f(x) = 0. It represents the x-intercepts of the graph.

Front

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

Back

If a zero has an even multiplicity, the graph will touch the x-axis at that zero and not cross it.

Front

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

Back

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

Front

How does the leading coefficient affect the end behavior of a polynomial graph?

Back

The leading coefficient determines whether the graph rises or falls as x approaches positive or negative infinity, depending on the degree being even or odd.

Front

What is the significance of the leading term in a polynomial function?

Back

The leading term, which is the term with the highest degree, dominates the behavior of the polynomial for large values of x.

Front

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

Back

A polynomial of degree n can have at most n-1 turning points.

Front

What is a turning point in the context of polynomial graphs?

Back

A turning point is a point on the graph where the direction of the graph changes from increasing to decreasing or vice versa.

Front

How can you determine the multiplicity of a zero from a polynomial's factored form?

Back

The multiplicity of a zero corresponds to the exponent of the factor associated with that zero in the polynomial's factored form.