y=1/2(x-3)^2-6

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Solution for y=1/2(x-3)^2-6 equation: 


x in (-oo:+oo)

y = (1/2)*(x-3)^2-6 // - (1/2)*(x-3)^2-6

y-((1/2)*(x-3)^2)+6 = 0

(-1/2)*(x-3)^2+y+6 = 0

y-1/2*(x-3)^2+6 = 0

y-1/2*(x-3)^2+6 = 0

3*x-1/2*x^2+y-9/2+6 = 0

3*x-1/2*x^2+y+3/2 = 0

3*x-1/2*x^2+y+3/2 = 0

3*x-1/2*x^2+y+3/2 = 0

DELTA = 3^2-(-1/2*4*(y+3/2))

DELTA = 2*(y+3/2)+9

2*(y+3/2)+9 = 0

2*(y+3/2)+9 = 0

2*y+12 = 0

2*y+12 = 0

2*y+12 = 0 // - 12

2*y = -12 // : 2

y = -12/2

y = -6

DELTA = 0  <=>  t_3 = -6

x = -3/(-1/2*2) i y = -6

x = 3 i y = -6

( x = ((2*(y+3/2)+9)^(1/2)-3)/(-1/2*2) or x = (-(2*(y+3/2)+9)^(1/2)-3)/(-1/2*2) ) i y > -6

( x = 3-(2*(y+3/2)+9)^(1/2) or x = (2*(y+3/2)+9)^(1/2)+3 ) i y > -6

y+6 > 0

y+6 > 0 // - 6

y > -6

x in { 3, 3-(2*(y+3/2)+9)^(1/2), (2*(y+3/2)+9)^(1/2)+3 }

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