Name: _________________________________ Period: _____ Date: ________
6.1-6.2 TAKE HOME QUIZ
*Due Tuesday January 31st*
Name each polynomial by degree and number of terms.
1. −10𝑟 3 − 8𝑟 2
2. 7
3. −9 + 7𝑛2 − 𝑛2 + 𝑛
4. (13𝑚4 + 2) + (𝑚3 + 2 − 2𝑚4 ) − (−13𝑚3 + 5𝑚4 )
5.
Critical Thinking: Why is it impossible to have a linear trinomial with one variable?
Describe the end behavior of each function.
6. 𝑓(𝑥) = −𝑥 5 + 4𝑥
7. 𝑓(𝑥) = 2𝑥 2 + 12𝑥 + 12
Write each function in standard form. Find the zeros (state multiplicity if necessary) and sketch the
graph of each function (hint: think about end behavior!).
8. 𝑝(𝑥) = (𝑥 − 5)(𝑥 + 5)(2𝑥 − 1)
9. 𝑦 = (𝑥 + 4)(2𝑥 − 5)(𝑥 + 5)2
Write each function in factored form. Find the zeros (state multiplicity if necessary) and sketch the graph
of each function (hint: think about end behavior!)
10. 𝑓(𝑥) = 𝑥 3 − 7𝑥 2 + 10𝑥
11. 𝑦 = 𝑥 4 − 𝑥 3 − 6𝑥 2
12. Use your graphing calculator to find a cubic function to model the data below (hint: use x = 0 to
represent the year 1940 and count up from there). Then use the function to estimate the average
monthly Social Security Benefit for a retired worker in 2005.
13. The diagram at the right shows a cologne bottle that consists of a cylindrical
base and a hemispherical top.
a. Write an expression for the cylinder’s volume (hint: if you forgot
formulas for volume, look in the “Skills Handbook” in the back of
your Algebra 2 textbook!).
b. Write an expression for the volume of the hemispherical top.
c. Write a polynomial to represent the total volume.
14. A metal worker wants to make an open box from a sheet of metal, by
cutting equal squares from each corner as shown.
a. Write an expression for the length, width, and height of the
open box.
b. Use your answer from part (a) to write a function for total
volume of the open box in standard form. (Hint: start with
factored form.)
c. Use your calculator to graph the function. Find the maximum volume (y) that can be contained
by the box and the size of the corner square cut (x) that produces this volume.
15. To start his project, a carpenter hollowed out the interior of a block of
wood as shown at the right.
a. Express the volume of the original block and the volume of the
wood removed as two polynomials in standard form.
b. Write a polynomial in standard form for the volume of the wood that is remaining.