1. **Stating the problem:** We need to graph the curve defined by the equation $x=1+2y^2$ and consider its revolution about the $y$-axis between $y=1$ and $y=2$. 2. **Understanding the curve:** The equation $x=1+2y^2$ describes a parabola opening to the right in the $xy$-plane. 3. **Revolution about the $y$-axis:** Revolving this curve about the $y$-axis creates a 3D surface. The radius of revolution at any $y$ is the $x$-value, $r = 1 + 2y^2$. 4. **Bounds:** The revolution is limited between $y=1$ and $y=2$. 5. **Graphing function for Desmos:** The curve itself is $x=1+2y^2$; for graphing in $xy$-plane, we use $y$ as the independent variable. Final answer: The curve is $x=1+2y^2$ for $y$ in $[1,2]$, revolved about the $y$-axis.