I figured it out
warning: mildly incoherent math logic ahead
ok, so if you want a parabola facing right, then
first I'll solve for up down standard parabola then reflect across x=y line
so
y=ax²+bx+c
so let's say teh vertex is at the origin
that means when x=0, y=0
0=0
c=0
y=ax²+bx
ok, see diagram
we have some points, (0,0) and (11,0.5) and (-11,0.5)
use those oints to find a and b
0.5=121a+11b
0.5=121a-11b
add dem equations
1=242a
divide by 242
1/242=a
subsitute
0.5=121a+11b
0.5=121(1/242)+11b
0.5=0.5+11b
0=11b
0=b
oook
de equaiton is
[tex]y= \frac{1}{242} x^2[/tex]
if we want it facing right
switch x and y
[tex]x= \frac{1}{242} y^2[/tex]
the equation is [tex]y= \frac{1}{242} x^2[/tex] or [tex]f(x)= \frac{1}{242} x^2[/tex] or [tex]x= \frac{1}{242} y^2[/tex] or [tex]f(y)= \frac{1}{242} y^2[/tex]
depends which way you want it and if you want f(x) or f(y) or x or y
