Algebra II – Level 1



Algebra II – Level 1 Name ________________________

Polynomial Functions HW: Worksheet 3.1

Relative Max/Min and End Behaviors (Lesson 6.2)

Questions in bold require a graphing calc.

1. Given: [pic]

a. State the degree f(x). Describe the end behaviors of the function.

b. Factor f(x).

c. Find the zeros of f(x).

d. Find the y-intercept.

e. Using the graphing calculator, find the ordered pairs that represent the relative maximum and minimum. Label them as such.

f. Sketch f(x). Labeling all key points mentioned above.

g. Find the Domain: ______________ Range: _______________

h. Interval(s) of increase: __________________ decrease: ________________

2. Given: [pic]

a. State the degree and describe the end behaviors of the given function.

b. Find the y-intercept.

c. Using the graphing calculator, find the zeros. Explain how you used the calculator to find the zeros.

d. Using the graphing calculator, find the ordered pairs that represent the relative maximum and minimum. Label them as such.

3. Rewrite each polynomial in factored form –factor by grouping. State the zeros of each factor and any multiplicities.

[pic]

a. [pic] b. [pic]

c. [pic] d. [pic]

4. Given: [pic]

a. State the degree and describe the end behavior of the given function.

b. Factor g(x).

c. Find the zeros.

d. Find [pic].

e. Using the graphing calculator, find the ordered pairs that represent the relative maximum and minimum. Label them as such. (It is possible to have more than one relative maximum or minimum.)

f. Sketch g(x). Label the key points found above.

g. Find the Domain: ___________ Range: ____________

h. State the interval(s) of increase: _______________ decrease: _____________

4. See the diagram for #15 and the initial description of the problem in your textbook p. 317

a. Write an expression for the length, width and height of the open box.

height: ______ length: ____________ width: ___________

b. Use your answer in part (a) to write a function for the volume of the box, V(x). Leave the function in its factored form.

c. Find the zeros.

d. A reasonable domain is (0, 6). Explain why the domain interval of (6, 8) is not reasonable. Explain why the domain interval of [pic]is not reasonable.

*e. Using the graphing calculator, find the maximum volume within the reasonable domain.

*f. What is the height of the box that produces the maximum volume?___________

Thus the dimensions of the square cut will be ________ by _____________.

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