Y=2/3(x-3)^2-4

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Solution for Y=2/3(x-3)^2-4 equation: 


x in (-oo:+oo)

Y = (2/3)*(x-3)^2-4 // - (2/3)*(x-3)^2-4

Y-((2/3)*(x-3)^2)+4 = 0

(-2/3)*(x-3)^2+Y+4 = 0

Y-2/3*(x-3)^2+4 = 0

Y-2/3*(x-3)^2+4 = 0

Y-2/3*x^2+4*x-6+4 = 0

Y-2/3*x^2+4*x-2 = 0

Y-2/3*x^2+4*x-2 = 0

Y-2/3*x^2+4*x-2 = 0

DELTA = 4^2-(-2/3*4*(Y-2))

DELTA = 8/3*(Y-2)+16

8/3*(Y-2)+16 = 0

8/3*(Y-2)+16 = 0

8/3*Y+32/3 = 0

8/3*Y+32/3 = 0

8/3*Y+32/3 = 0 // - 32/3

8/3*Y = -32/3 // : 8/3

Y = -32/3/8/3

Y = -4

DELTA = 0  <=>  t_3 = -4

x = -4/(-2/3*2) i Y = -4

x = 3 i Y = -4

( x = ((8/3*(Y-2)+16)^(1/2)-4)/(-2/3*2) or x = (-(8/3*(Y-2)+16)^(1/2)-4)/(-2/3*2) ) i Y > -4

( x = -3/4*((8/3*(Y-2)+16)^(1/2)-4) or x = 3/4*((8/3*(Y-2)+16)^(1/2)+4) ) i Y > -4

Y+4 > 0

Y+4 > 0 // - 4

Y > -4

x in { 3, -3/4*((8/3*(Y-2)+16)^(1/2)-4), 3/4*((8/3*(Y-2)+16)^(1/2)+4) }

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