Graphs of Polynomials Worksheet

Explore the graphs of polynomial functions, including their end behavior, roots, multiplicity, and turning points.

Grade 10 Math AlgebraGraphs of Polynomials

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Multiple ChoiceFill in the BlanksShort AnswerCustomTrue / False

Standards

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

Topics

polynomialsgraphsalgebragrade 10

7 sections · Free to use · Printable

Graphs of Polynomials

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Read each question carefully and provide your answer in the space provided. For graphing questions, use the coordinate plane. Show all your work.

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

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

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

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

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

2. What is the maximum number of turning points a polynomial of degree 4 can have?

3. If a polynomial function has a root with an even multiplicity, its graph will the x-axis at that root.

4. The degree of a polynomial determines its behavior.

5. Describe the relationship between the degree of a polynomial function and the maximum number of x-intercepts it can have.

6. Sketch the graph of the polynomial function f(x) = (x - 1)^2 (x + 2). Label the x-intercepts and describe the end behavior.

7. A polynomial function with an odd degree must have at least one real root.

True

False