y=-(1/2)(x-5)^2-3

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Solution for y=-(1/2)(x-5)^2-3 equation: 


x in (-oo:+oo)

y = -((1/2)*(x-5)^2)-3 // + -((1/2)*(x-5)^2)-3

(1/2)*(x-5)^2+y+3 = 0

1/2*(x-5)^2+y+3 = 0

1/2*(x-5)^2+y+3 = 0

1/2*x^2-5*x+y+3+25/2 = 0

1/2*x^2-5*x+y+31/2 = 0

1/2*x^2-5*x+y+31/2 = 0

1/2*x^2-5*x+y+31/2 = 0

DELTA = (-5)^2-(1/2*4*(y+31/2))

DELTA = 25-2*(y+31/2)

25-2*(y+31/2) = 0

25-2*(y+31/2) = 0

-2*y-6 = 0

-2*y-6 = 0

-2*y-6 = 0 // + 6

-2*y = 6 // : -2

y = 6/(-2)

y = -3

DELTA = 0  <=>  t_3 = -3

x = 5/(1/2*2) i y = -3

x = 5 i y = -3

( x = ((25-2*(y+31/2))^(1/2)+5)/(1/2*2) or x = (5-(25-2*(y+31/2))^(1/2))/(1/2*2) ) i y > -3

( x = (25-2*(y+31/2))^(1/2)+5 or x = 5-(25-2*(y+31/2))^(1/2) ) i y > -3

y+3 > 0

y+3 > 0 // - 3

y > -3

x in { 5, (25-2*(y+31/2))^(1/2)+5, 5-(25-2*(y+31/2))^(1/2) }

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