Exploring the equation for the volume of the box leads to many discoveries (such as the largest value x can be on the given cardboard is 7.5). The maximum volume of the box is where the parabola reaches its maximum value. Overlaying the graph Y=400 on the existing parabola will cross the parabola at the values of X that produce the volume of 400 cubic inches.

 

 

From the graph, the maximum value is approx. 500 cubic inches and the values of X yielding a volume of 400 cubic inches are approx. 1.6 inches and 4.75 inches.