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

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

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

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

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

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

5*x-1/2*x^2+y-19/2 = 0

5*x-1/2*x^2+y-19/2 = 0

5*x-1/2*x^2+y-19/2 = 0

DELTA = 5^2-(-1/2*4*(y-19/2))

DELTA = 2*(y-19/2)+25

2*(y-19/2)+25 = 0

2*(y-19/2)+25 = 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 = ((2*(y-19/2)+25)^(1/2)-5)/(-1/2*2) or x = (-(2*(y-19/2)+25)^(1/2)-5)/(-1/2*2) ) i y > -3

( x = 5-(2*(y-19/2)+25)^(1/2) or x = (2*(y-19/2)+25)^(1/2)+5 ) i y > -3

y+3 > 0

y+3 > 0 // - 3

y > -3

x in { 5, 5-(2*(y-19/2)+25)^(1/2), (2*(y-19/2)+25)^(1/2)+5 }

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