Each of the following equations is of the form $y=-\frac{1}{2}{x}^p(x+1{)}^q(x-2{)}^r$, where $p$, $q$, and $r$ are positive integers. The graph of such a function has x-intercepts at $x=-1,x=0,$ and $x=2$. For a certain function of this form, the graph has $y>0$ for all $x<-1$ and $y<0$ for all $x>2$. Which of the following equations could represent this function?