1. Applications of Cubic Functions

2. Volume of a Open Box.
Suppose you are trying to make an open-top box out of a piece of cardboard that is 20 inches by 16 inches. You are to cut the same size square from each corner. Write a function to represent the volume of this box. 20 x
20 - 2x
16 - 2x 16

3. V=lwh
20 - 2x ? x
16 - 2x
20 - 2x

4. Formula for the Volume of a Box
The final answer for the volume will ALWAYS have the term :

5. Write the formula for the volume of our box:
Step 1: Multiply the two binomials together
Step 2: Multiply by x 20
-2x 16
320
-40x
-32x
4x2

6. What is the maximum volume?
What is the possible domain for this box? What is the greatest possible value that we can cut out for x?
0 < X < 8 (Half of the length of the smallest side)
SO, Xmin = 0 and Xmax = 8; ZOOM 0
Do you want x or y?
Y!!!
420 cubic inches

7. What size square should be cut from each corner to realize the maximum volume?
What do you want now?
X!!
2.9 inches

8. Y!! Let y = 300; find the intersection
What size square should you cut from each corner to realize a volume of 300 cubic inches?
What do you know: x or y?
Y!! Let y = 300; find the intersection
1.3 inches or 5 inches

9. What is the volume if a square with side 2 inches is cut from each corner?
What do you know; x or y?
X!!!
Go to table; let x = 2
384 Cubic inches