y=-1/2x^2+x+4

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Solution for y=-1/2x^2+x+4 equation: 


x in (-oo:+oo)

y = (-1/2)*x^2+x+4 // - (-1/2)*x^2+x+4

y-((-1/2)*x^2)-x-4 = 0

(1/2)*x^2-x+y-4 = 0

1/2*x^2-x+y-4 = 0

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

DELTA = 1-2*(y-4)

1-2*(y-4) = 0

1-2*(y-4) = 0

9-2*y = 0

9-2*y = 0

9-2*y = 0 // - 9

-2*y = -9 // : -2

y = -9/(-2)

y = 9/2

DELTA = 0  <=>  t_1 = 9/2

x = 1/(1/2*2) i y = 9/2

x = 1 i y = 9/2

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

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

y-9/2 > 0

y-9/2 > 0 // + 9/2

y > 9/2

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

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