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

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


x in (-oo:+oo)

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

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

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

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

3*x-3*x^2+y-5-3/4 = 0

3*x-3*x^2+y-23/4 = 0

3*x-3*x^2+y-23/4 = 0

3*x-3*x^2+y-23/4 = 0

DELTA = 3^2-(-3*4*(y-23/4))

DELTA = 12*(y-23/4)+9

12*(y-23/4)+9 = 0

12*(y-23/4)+9 = 0

12*y-60 = 0

12*y-60 = 0

12*y-60 = 0 // + 60

12*y = 60 // : 12

y = 60/12

y = 5

DELTA = 0  <=>  t_3 = 5

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

x = 1/2 i y = 5

( x = ((12*(y-23/4)+9)^(1/2)-3)/(-3*2) or x = (-(12*(y-23/4)+9)^(1/2)-3)/(-3*2) ) i y > 5

( x = ((12*(y-23/4)+9)^(1/2)-3)/(-6) or x = ((12*(y-23/4)+9)^(1/2)+3)/6 ) i y > 5

y-5 > 0

y-5 > 0 // + 5

y > 5

x in { 1/2, ((12*(y-23/4)+9)^(1/2)-3)/(-6), ((12*(y-23/4)+9)^(1/2)+3)/6 }

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