Finding Polynomial Functions from Graphs

Grade 12 math worksheet on determining polynomial functions given their graphs, focusing on roots, multiplicity, and end behavior.

Grade 12 Math AlgebraFinding Polynomial Function From a Graph

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3 CustomTrue / FalseFill in the Blanks

Standards

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

7 sections · Free to use · Printable

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Finding Polynomial Functions from Graphs

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Analyze each graph to determine the characteristics of the polynomial function. Then, write the equation of the polynomial function in factored form. Show all your work.

1. Consider the graph of a polynomial function shown below. Identify the roots, their multiplicities, and describe the end behavior. Then, write the equation of the polynomial function.

Roots and Multiplicities:

End Behavior:

Equation of the Polynomial Function:

2. For the polynomial function graphed below, determine the degree, leading coefficient sign, and find its equation in factored form.

Degree:

Sign of Leading Coefficient:

Equation of the Polynomial Function:

3. The graph of a polynomial function has x-intercepts at (-2, 0), (1, 0), and (3, 0). The graph touches the x-axis at x = 1 and crosses at x = -2 and x = 3. The y-intercept is (0, 12). Write the equation of this polynomial function.

Equation of the Polynomial Function:

4. If a polynomial graph crosses the x-axis at a root, its multiplicity must be odd.

True

False

5. The end behavior of a polynomial function is determined by its and .