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

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


x in (-oo:+oo)

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

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

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

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

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

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

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

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

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

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

DELTA = 4-2*(y-1)

4-2*(y-1) = 0

4-2*(y-1) = 0

6-2*y = 0

6-2*y = 0

6-2*y = 0 // - 6

-2*y = -6 // : -2

y = -6/(-2)

y = 3

DELTA = 0  <=>  t_3 = 3

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

x = 2 i y = 3

( x = ((4-2*(y-1))^(1/2)+2)/(1/2*2) or x = (2-(4-2*(y-1))^(1/2))/(1/2*2) ) i y > 3

( x = (4-2*(y-1))^(1/2)+2 or x = 2-(4-2*(y-1))^(1/2) ) i y > 3

y-3 > 0

y-3 > 0 // + 3

y > 3

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

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