Question 366722
It would be of the form {{{x = -ay^2 + by + c}}}
If the vertex is at the origin, then I can write
{{{0 = -a*0 + b*0 + c}}}, so {{{c = 0}}}
If it includes (-3/2,1),
{{{-3/2 = -a*1^2 + b*1}}}
(1) {{{b - a = -3/2}}}
By symmetry, it must also pass through (-3/2,-1), so
{{{-3/2 = -a(-1)^2 + b*(-1)}}}
(2) {{{-b - a = -3/2}}}
Add (1) and (2)
{{{-2a = -3}}}
{{{a = 3/2}}}
And, since
(1) {{{b - a = -3/2}}}
{{{b = -3/2 + a}}}
{{{b = -3/2 + 3/2}}}
{{{b = 0}}}
The equation is
{{{x = -(3/2)*y^2}}}