Box Folding: Formulas and graphs

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

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?

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