[size=150][size=200]I want to build square cross sections between the parabola and the x-axis.[br]1. Enter the function. I entered [b]f(x) = -(x-1)(x-6). [/b]I did not use a doman restriction.[br]2. This only works if the EDGES of the solid are formed using parametric equations. This is the CURVE() command in GeoGebra.[br]3. Enter a[b] = curve(t,f(t),0,t,1,6)[/b]. This is the functions expressed parametrically. [br]Parametrically, this is x(t) = t, y(t) = f(t), z(t) = 0, as [br]t varies from 1 to 6[br]4. By habit, I name the edge ABOVE [b]a[/b] as [b]aa[/b].[br]Enter aa=curve(t,f(t),f(t),t,1,6)[br]5. Then, enter b=curve(t,0,0,t,1,6) for the edge along the x-axis[br]6. Enter bb=curve(t,0,f(t),t,1,6) for the edge above b.[/size][/size]

[size=200]To graph the top surface, enter [br][b]Surface( u aa(t) + (1-u) bb(t), u,0,1,t,1,6)[br][/b]Think of this as the parameter u being used to stretch one curve to another.[/size]

[size=200]To graph the rear surface, enter [br][b]Surface( u a(t) + (1-u) aa(t), u,0,1,t,1,6)[br][/b][/size]

[size=200]To graph the bottom surface, enter [br][b]Surface( u a(t) + (1-u) b(t), u,0,1,t,1,6)[br][/b][/size]

[size=200]To graph the front surface, enter [br][b]Surface( u b(t) + (1-u) bb(t), u,0,1,t,1,6)[br][/b][/size]