Y=1/2(x-4)^2-2

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Solution for Y=1/2(x-4)^2-2 equation: 


x in (-oo:+oo)

Y = (1/2)*(x-4)^2-2 // - (1/2)*(x-4)^2-2

Y-((1/2)*(x-4)^2)+2 = 0

(-1/2)*(x-4)^2+Y+2 = 0

Y-1/2*(x-4)^2+2 = 0

Y-1/2*(x-4)^2+2 = 0

Y-1/2*x^2+4*x-8+2 = 0

Y-1/2*x^2+4*x-6 = 0

Y-1/2*x^2+4*x-6 = 0

Y-1/2*x^2+4*x-6 = 0

DELTA = 4^2-(-1/2*4*(Y-6))

DELTA = 2*(Y-6)+16

2*(Y-6)+16 = 0

2*(Y-6)+16 = 0

2*Y+4 = 0

2*Y+4 = 0

2*Y+4 = 0 // - 4

2*Y = -4 // : 2

Y = -4/2

Y = -2

DELTA = 0  <=>  t_3 = -2

x = -4/(-1/2*2) i Y = -2

x = 4 i Y = -2

( x = ((2*(Y-6)+16)^(1/2)-4)/(-1/2*2) or x = (-(2*(Y-6)+16)^(1/2)-4)/(-1/2*2) ) i Y > -2

( x = 4-(2*(Y-6)+16)^(1/2) or x = (2*(Y-6)+16)^(1/2)+4 ) i Y > -2

Y+2 > 0

Y+2 > 0 // - 2

Y > -2

x in { 4, 4-(2*(Y-6)+16)^(1/2), (2*(Y-6)+16)^(1/2)+4 }

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