Hi all.

I need to fit a parabola to some constraints. Again.
I know one point on the curve (x1,y1)
I know that the gradient at that point is 0.
I know the radius of curvature of that parabola.

y=ax²+bx+c (1)
y’=2ax+b (2)
y’’=2a (3)
Curvature = 1/Radius (4)

(3)=(4)
2a=1/Radius
a=1/(2*Radius) (5)

Gradient=0 so from (2) and substituting (5)
0=2*1/(2*Radius) * X1 + b
b=-x1/Radius (6)

At the known point x1,y1, from (1) substituting (5) and (6)
y1=1/(2*Radius)*(x1)²-x1/Radius*x1+c
y1=(x1)²/(2*Radius) - (x1)²/Radius+c
y1=(x1)²/(2*Radius) - 2 (x1)²/(2*Radius)+c
y1=-(x1)²/(2*Radius)+c
c=y1+(x1)²/(2*Radius)

Now say x1=8000 y1=250 Radius=-5500
a=-0.0001
b=1.4545
c=-5568
So the equation of the curve is:
y=-0.0001x²+1.4545x-5568
So why does
y=-0.0001*(8000)²+1.4545*8000-5568=-332 when it should equal 250
Where have I gone wrong?