jmc

The y-intercept of a function is the value of the function when $x=0$. Thus, we want to find the value of $Q(0)=P(0{)}^2$. Now, $P(0)=4(0{)}^3-2(0{)}^2+7(0)-1=-1$, so it follows that $Q(0)=(-1{)}^2=\boxed{1}$.