  We consider quadratic optimization in variables $(x,y)$ where $0\le x\le y$,
and $y\in\{0,1\}^n$. Such binary $y$ are commonly refered to as "indicator" or
"switching" variables and occur commonly in applications. One approach to such
problems is based on representing or approximating the convex hull of the set
$\{ (x,xx^T, yy^T) : 0\le x\le y\in\{0,1\}^n\}$. A representation for the case
$n=1$ is known and has been widely used. We give an exact representation for
the case $n=2$ by starting with a disjunctive representation for the convex
hull and then eliminating auxilliary variables and constraints that do not
change the projection onto the original variables. An alternative derivation
for this representation leads to an appealing conjecture for a simplified
representation of the convex hull for $n=2$ when the product term $y_1y_2$ is
ignored.
