Finding Polynomial Function From a Graph
Grade 10 Math worksheet on determining polynomial functions from their graphs, focusing on roots, multiplicity, and end behavior.
Includes
Standards
Finding Polynomial Function From a Graph
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Analyze each graph to determine the characteristics of the polynomial function. Then, write the possible equation for the polynomial function in factored form.
1. Consider the graph below. Identify the roots and their multiplicities, describe the end behavior, and write a possible equation for the polynomial function.
Roots and Multiplicities:
End Behavior:
Possible Equation:
2. For the polynomial graph shown, determine the roots and their multiplicities, describe the end behavior, and write a possible equation for the polynomial function.
Roots and Multiplicities:
End Behavior:
Possible Equation:
3. Which of the following polynomial functions could represent a graph that crosses the x-axis at x = -2, touches the x-axis at x = 1, and has end behavior where both ends go up?
f(x) = (x+2)(x-1)^2
f(x) = -(x+2)(x-1)^2
f(x) = (x-2)(x+1)^2
f(x) = -(x-2)(x+1)^2
4. If a polynomial graph crosses the x-axis at a point, the corresponding root has an even multiplicity.
True
False
5. A polynomial graph that touches the x-axis at a root but does not cross it indicates that the root has an multiplicity.