# Square Cross Sections Perpendicular to x-Axis

- Author:
- Steve Phelps

- Topic:
- Square

I want to build square cross sections between the parabola and the x-axis.
1. Enter the function. I entered

**f(x) = -(x-1)(x-6).**I did not use a doman restriction. 2. This only works if the EDGES of the solid are formed using parametric equations. This is the CURVE() command in GeoGebra. 3. Enter a**= curve(t,f(t),0,t,1,6)**. This is the functions expressed parametrically. Parametrically, this is x(t) = t, y(t) = f(t), z(t) = 0, as t varies from 1 to 6 4. By habit, I name the edge ABOVE**a**as**aa**. Enter aa=curve(t,f(t),f(t),t,1,6) 5. Then, enter b=curve(t,0,0,t,1,6) for the edge along the x-axis 6. Enter bb=curve(t,0,f(t),t,1,6) for the edge above b.To graph the top surface, enter

**Surface( u aa(t) + (1-u) bb(t), u,0,1,t,1,6)**Think of this as the parameter u being used to stretch one curve to another.To graph the rear surface, enter

**Surface( u a(t) + (1-u) aa(t), u,0,1,t,1,6)**To graph the bottom surface, enter

**Surface( u a(t) + (1-u) b(t), u,0,1,t,1,6)**To graph the front surface, enter

**Surface( u b(t) + (1-u) bb(t), u,0,1,t,1,6)**