SOLUTION: I've got this question: An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: I've got this question: An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let      Log On


   

Question 44025: I've got this question: An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out.
a)Find the function V that represents the volume of the box in terms of x.

I've managed to come up with volume of the box is width x length x height = (6-2x)(8-2x)x. This is where it ends for me, I can't figure out how to solve it and I need to solve it, because I have to graph it.

b) Graph this function and show the graph over the valid range of the variable x.
PLEASE PLEASE HELP!
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Well, you've a good start!
V+=+%286-2x%29%288-2x%29x Now continue by multiplying the three factors here to get the equation for the volume, v, in terms of x.
V+=+4x%5E3-28x%5E2%2B48x Now you can graph this equation using a graphing calculator. The graph looks like this:
graph%28300%2C200%2C-5%2C5%2C-10%2C25%2C4x%5E3-28x%5E2%2B48x%29
The valid range of x would be:
0%3Cx%3C3
Because, if:x%3C=0 or x%3E=3 the volume would be zero or negative, and this is not meaningful.