Zeros and Multiplicity Worksheet
Explore zeros of polynomial functions, their multiplicities, and how they affect the graph's behavior at the x-axis.
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Zeros and Multiplicity
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. What is the multiplicity of the zero x = 3 in the polynomial function f(x) = (x-3)^2 (x+1)?
1
2
3
4
2. If a zero has an even multiplicity, how does the graph of the polynomial function behave at the x-axis?
It crosses the x-axis
It touches the x-axis and turns around
It is tangent to the x-axis
Both b and c
3. The of a zero is the number of times its corresponding factor appears in the factored form of the polynomial.
4. If a zero has an odd multiplicity, the graph of the polynomial function the x-axis at that point.
5. Find the zeros and their multiplicities for the polynomial function f(x) = x^3 - 4x^2 + 4x.
6. Describe the behavior of the graph of f(x) = (x+2)^3 (x-1)^2 at each of its zeros.
7. Sketch a possible graph of a polynomial function with zeros at x = -3 (multiplicity 1), x = 0 (multiplicity 2), and x = 2 (multiplicity 3).