Graphs of Polynomial Functions
Describe the end behavior of the polynomial function by stating if the graph goes up or down on the far left and up or down on the far right.
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| 1) Describe the end behavior of the polynomial function.
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| 2) Describe the end behavior of the polynomial function.
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| 3) Describe the end behavior of the polynomial function.
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| 4) Describe the end behavior of the polynomial function.
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Refer to the graph below to answer the following questions about the polynomial function.
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| 5) What is the end behavior of the polynomial function?
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| 6) What type of polynomial does the graph represent?
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| 7) What type of leading coefficient does the polynomial have?
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| 8) How many real roots does the polynomial function have?
Hint: How many times does the graph cross the x-axis?
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Refer to the graph below to answer the following questions about the polynomial function.
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| 9) What is the end behavior of the polynomial function?
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| 10) What type of polynomial does the graph represent?
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| 11) What type of leading coefficient does the polynomial have?
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| 12) How many real roots does the polynomial function have?
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Refer to the graph below to answer the following questions about the polynomial function.
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| 13) What is the end behavior of the polynomial function?
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| 14) What type of polynomial does the graph represent?
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| 15) What type of leading coefficient does the polynomial have?
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| 16) How many real roots does the polynomial function have?
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Solving Polynomial Equations by Factoring
For the following problems, use factoring to solve the equation.
Hint: The right side of the equation must be equal to zero. Then factor out the GCF.
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| 17) Solve for x.
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| 18) Solve for y.
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| 19) Solve for x.
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| 20) Solve for y.
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Solving Polynomial Equations by Using a Graph and Synthetic Division
For the following problems, use a graph, synthetic division, and factoring to find all of the real roots of the equation. State each root and its multiplicity.
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| 21) Solve for x.
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| 22) Solve for x.
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| 23) Solve for x.
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| 24) Solve for x.
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Writing a Polynomial Function
For the following problems, write a polynomial function (P) in standard form by using the given information.
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| 25) Write the polynomial function for the given information.
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| 26) Write the polynomial function for the given information.
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| 27) When P(x) touches but does not cross the x-axis at (r, 0), what must be true of P(x)? Give an example of a polynomial for which this is true.
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| 28) Write an equation for a polynomial that fits the following description: it has a degree 3 and the graph goes up to the far left and down to the far right.
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| 31) Evaluate the expression 5x3 + 2x2 – 5x + 12 for x = –2.
Click here to review the unit content explanation for Polynomial Functions.
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| 32) True or false? The linear expression x + 3 is a factor of the given polynomial.
Click here to review the unit content explanation for Polynomial Functions.
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| 34) Extended Learning
Watch the following video, then write a five-sentence paragraph summarizing the video.
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| 35) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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