Question 916939
This is mostly just symbolic substitution and then simple algebraic steps.


Put the function into standard form using your given information.


{{{highlight_green(f(x)=a(x-Vx)^2+Vy)}}}, and as you, I am continuing to assume the lower case character in the mixed notation is like a subscript.


Wanting the roots, just equate f(x) to 0.
{{{a(x-Vx)^2+Vy=0}}}
Solve for "x".


{{{a(x-Vx)^2=-Vy}}}
{{{(x-Vx)^2=-(1/a)Vy}}}
.
{{{x=Vx+- sqrt(-Vy/a)}}}
.
{{{x=Vx+- (1/a)sqrt(-Vy*a)}}}


You really want to make sure your subscripts "look like" subscripts and not simply extra attached variables; so you really should show...
{{{highlight(x=V[x]+- (1/a)sqrt(-V[y]*a))}}}