Finding Polynomial Functions from Graphs

This worksheet helps Grade 11 students practice identifying key features of polynomial graphs and using them to construct polynomial functions.

Grade 11 Math AlgebraFinding Polynomial Function From a Graph

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2 Short AnswerMultiple ChoiceFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HSA.APR.B.3CCSS.MATH.CONTENT.HSA.CED.A.2

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Finding Polynomial Functions from Graphs

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Carefully analyze each graph of a polynomial function. Identify the zeros, their multiplicities, and the end behavior. Use this information to write a possible equation for the polynomial function in factored form. Assume the leading coefficient is 1 unless otherwise specified.

1. Analyze the graph below and write a possible polynomial function in factored form.

Zeros and Multiplicities:

End Behavior:

Possible Function f(x) =

2. Which of the following polynomial functions could represent the graph shown?

f(x) = (x+2)(x-1)(x-3)

f(x) = -(x+2)(x-1)(x-3)

f(x) = (x+2)^2(x-1)(x-3)

f(x) = (x-2)(x+1)(x+3)

3. If a polynomial graph touches the x-axis at a zero and turns around, the multiplicity of that zero is .

4. If a polynomial graph crosses the x-axis at a zero, the multiplicity of that zero is .

5. For a polynomial with an odd degree and a positive leading coefficient, the end behavior is as x → -∞, f(x) → and as x → +∞, f(x) → .

6. A polynomial function of degree 'n' can have at most 'n' real zeros.

True

False

7. Consider a polynomial graph that goes down on the left and up on the right. What can you conclude about its degree and leading coefficient?