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

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


x in (-oo:+oo)

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

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

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

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

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

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

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

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

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

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

DELTA = 2*(y-1)+4

2*(y-1)+4 = 0

2*(y-1)+4 = 0

2*y+2 = 0

2*y+2 = 0

2*y+2 = 0 // - 2

2*y = -2 // : 2

y = -2/2

y = -1

DELTA = 0  <=>  t_3 = -1

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

x = -2 i y = -1

( x = ((2*(y-1)+4)^(1/2)+2)/(-1/2*2) or x = (2-(2*(y-1)+4)^(1/2))/(-1/2*2) ) i y > -1

( x = -((2*(y-1)+4)^(1/2)+2) or x = (2*(y-1)+4)^(1/2)-2 ) i y > -1

y+1 > 0

y+1 > 0 // - 1

y > -1

x in { -2, -((2*(y-1)+4)^(1/2)+2), (2*(y-1)+4)^(1/2)-2 }

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