Graphs of Polynomials Worksheet

Explore the graphs of polynomial functions, identifying key features such as degree, leading coefficient, end behavior, zeros, and multiplicity.

Grade 9 Math AlgebraGraphs of Polynomials

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Multiple ChoiceFill in the BlanksShort AnswerTrue / FalseCustom

Standards

CCSS.MATH.CONTENT.HSA.APR.B.3CCSS.MATH.CONTENT.HSF.IF.C.7.C

7 sections · Free to use · Printable

Graphs of Polynomials

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Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. Which of the following describes the end behavior of the polynomial function f(x) = -2x^3 + 5x^2 - x + 7?

As x → ∞, f(x) → ∞; as x → -∞, f(x) → ∞

As x → ∞, f(x) → -∞; as x → -∞, f(x) → -∞

As x → ∞, f(x) → -∞; as x → -∞, f(x) → ∞

As x → ∞, f(x) → ∞; as x → -∞, f(x) → -∞

2. What is the maximum number of real zeros a polynomial of degree 4 can have?

3. The graph of a polynomial function with an odd degree and a positive leading coefficient will fall on the left and on the right.

4. If a zero of a polynomial has an even multiplicity, the graph will the x-axis at that point.

5. Describe the relationship between the degree of a polynomial and the maximum number of turning points its graph can have.

6. A polynomial function can have more x-intercepts than its degree.

True

False

7. Consider the graph of the polynomial function shown below. Identify the approximate real zeros and discuss the possible multiplicity of each zero.