Zeros & Multiplicity

Front

What does it mean if the graph of a function crosses the x-axis?

Back

The zero at that point has an odd multiplicity.

Front

What does it mean if there is a turning point on the x-axis?

Back

The zero at that point has an even multiplicity.

Front

Write a polynomial function rule for zeros at 5 (multiplicity 2), 3 (multiplicity 1), and 0 (multiplicity 4).

Back

Front

Classify the function with the highest degree of 3. What is it called?

Back

Cubic function.

Front

Identify the real zeros and their multiplicities for the function f(x) = x^2(x - 2)^3(x - 7).

Back

0 (Multiplicity 2), 2 (Multiplicity 3), 7 (Multiplicity 1).

Front

What is the multiplicity of a zero if the graph touches the x-axis but does not cross it?

Back

The multiplicity is even.

Front

What is the multiplicity of a zero if the graph crosses the x-axis?

Back

The multiplicity is odd.

Front

If a polynomial has a zero at x = -4 with multiplicity 3, how does the graph behave at this zero?

Back

The graph will cross the x-axis and have a point of inflection at x = -4.

Front

What is the general form of a polynomial function with zeros at x = a, b, and c?

Back

Front

How do you determine the multiplicity of a zero from a polynomial equation?

Back

The multiplicity is determined by the exponent of the factor corresponding to that zero.