y=-1/2x^2+x-1

Solution for y=-1/2x^2+x-1 equation:

x in (-oo:+oo)

y = (-1/2)*x^2+x-1 // - (-1/2)*x^2+x-1

y-((-1/2)*x^2)-x+1 = 0

(1/2)*x^2-x+y+1 = 0

1/2*x^2-x+y+1 = 0

DELTA = (-1)^2-(1/2*4*(y+1))

DELTA = 1-2*(y+1)

1-2*(y+1) = 0

1-2*(y+1) = 0

-2*y-1 = 0

-2*y-1 = 0

-2*y-1 = 0 // + 1

-2*y = 1 // : -2

y = 1/(-2)

y = -1/2

DELTA = 0  <=>  t_1 = -1/2

x = 1/(1/2*2) i y = -1/2

x = 1 i y = -1/2

( x = ((1-2*(y+1))^(1/2)+1)/(1/2*2) or x = (1-(1-2*(y+1))^(1/2))/(1/2*2) ) i y > -1/2

( x = (1-2*(y+1))^(1/2)+1 or x = 1-(1-2*(y+1))^(1/2) ) i y > -1/2

y+1/2 > 0

y+1/2 > 0 // - 1/2

y > -1/2

x in { 1, (1-2*(y+1))^(1/2)+1, 1-(1-2*(y+1))^(1/2) }