Tucson Workshop
Phil, Mary Kay, Amy, Kathy & Leslie
Polynomial Question
A box can be created from a rectangular piece of cardboard by removing a
square from each corner. Referring to the expression (22  2 x)(19  2 x)( x) and the
diagram, answer the following questions:
22 centimeters
19 centimeters
1. What does the 22 represent in this situation?
2. What does the 2x represent in this situation?
3. Label each dimension of the box with the appropriate factor from the
expression.
4. What does the entire expression represent with relation to the box?
5. What are the constraints to how small x can be?
6. What are the constraints to how large x can be?
Homework
1. Write this expression as a function V in terms of x.
2. What would be a reasonable window for your horizontal axis to graph this
function?
3. Graph the function and sketch it below.
4. What is the maximum? What does this mean in the context of the
problem.
Tucson Workshop
Phil, Mary Kay, Amy, Kathy & Leslie
Explaining Exponents
Determine if the value of the expression will always be positive, always be
negative, or will vary. Define the conditions that will determine the sign.
1. x  y
2. y  x
3. x  y
x
4.
y
5. x 2
6. x 3
7.  x 2
8. ( x) 2
9.  x 3
10. ( x) 3
11. ( x  y ) 2
12. x 2  y 2