y=1/2(x+5)^2-9

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Solution for y=1/2(x+5)^2-9 equation: 


x in (-oo:+oo)

y = (1/2)*(x+5)^2-9 // - (1/2)*(x+5)^2-9

y-((1/2)*(x+5)^2)+9 = 0

(-1/2)*(x+5)^2+y+9 = 0

y-1/2*(x+5)^2+9 = 0

y-1/2*(x+5)^2+9 = 0

y-1/2*x^2-5*x-25/2+9 = 0

y-1/2*x^2-5*x-7/2 = 0

y-1/2*x^2-5*x-7/2 = 0

y-1/2*x^2-5*x-7/2 = 0

DELTA = (-5)^2-(-1/2*4*(y-7/2))

DELTA = 2*(y-7/2)+25

2*(y-7/2)+25 = 0

2*(y-7/2)+25 = 0

2*y+18 = 0

2*y+18 = 0

2*y+18 = 0 // - 18

2*y = -18 // : 2

y = -18/2

y = -9

DELTA = 0  <=>  t_3 = -9

x = 5/(-1/2*2) i y = -9

x = -5 i y = -9

( x = ((2*(y-7/2)+25)^(1/2)+5)/(-1/2*2) or x = (5-(2*(y-7/2)+25)^(1/2))/(-1/2*2) ) i y > -9

( x = -((2*(y-7/2)+25)^(1/2)+5) or x = (2*(y-7/2)+25)^(1/2)-5 ) i y > -9

y+9 > 0

y+9 > 0 // - 9

y > -9

x in { -5, -((2*(y-7/2)+25)^(1/2)+5), (2*(y-7/2)+25)^(1/2)-5 }

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