Box Folding: Formulas and Graphs

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If you express the volume of a box (made from 22 x 18 grid paper described earlier) as an equation with height  x, then the length is 22-2x (why? ) and the width is 18-2x.

x*(22-2x)(18-2x) can be plugged into your graphing calculator and plotted.
It will look like the plots below.

graphing calculator equations
The graph of  x*(22-2x)*(18-2x) is at left.
calculator window settings
The window settings on the calculator look like those at left.

Considering the actual the boxes folded, what does it mean when the graph dips below the x-axis?

Now, take a look at the graph below. It comes from an Excel spreadsheet

excel graph with trendline and equation
Above is a trendline added to the Excel graph of the volume of the boxes. How is the equation that Excel gives related to the equation we used in the graphing calculator?