Question 33623
The dimension of the rectangular cardboard is 6 ft X 8 ft
Let x-ft be each side of the square cut out from each of the four corners.
The length of the open-top box would be (8-2x) ft (Note: two corners);
The width of the open-top box would be (6-2x) ft.
The height of the open-top box would be x ft. (if you draw a diagram, it will neatly explain the resulting dimension of the open-top box);
The voume of a box = Length X Width X Height;
If V(x) represents the volume function of the box:
V(x) = x(8-2x)(6-2x);
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As far as graphing goes, this is a polynomial of degree 3. This is also bound by the restriction (domain of the function) x >= 0 and x <= 3;
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