Y=5/4(x-3)^2

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Solution for Y=5/4(x-3)^2 equation: 


x in (-oo:+oo)

Y = (5/4)*(x-3)^2 // - (5/4)*(x-3)^2

Y-((5/4)*(x-3)^2) = 0

(-5/4)*(x-3)^2+Y = 0

Y-5/4*(x-3)^2 = 0

Y-5/4*(x-3)^2 = 0

Y-5/4*x^2+15/2*x-45/4 = 0

Y-5/4*x^2+15/2*x-45/4 = 0

Y-5/4*x^2+15/2*x-45/4 = 0

DELTA = (15/2)^2-(-5/4*4*(Y-45/4))

DELTA = 5*(Y-45/4)+225/4

5*(Y-45/4)+225/4 = 0

(4*5*(Y-45/4))/4+225/4 = 0

4*5*(Y-45/4)+225 = 0

20*Y = 0

(20*Y)/4 = 0

(20*Y)/4 = 0 // * 4

20*Y = 0

20*Y = 0 // : 20

Y = 0

DELTA = 0  <=>  t_3 = 0

x = -15/2/(-5/4*2) i Y = 0

x = 3 i Y = 0

( x = ((5*(Y-45/4)+225/4)^(1/2)-15/2)/(-5/4*2) or x = (-(5*(Y-45/4)+225/4)^(1/2)-15/2)/(-5/4*2) ) i Y > 0

( x = -2/5*((5*(Y-45/4)+225/4)^(1/2)-15/2) or x = 2/5*((5*(Y-45/4)+225/4)^(1/2)+15/2) ) i Y > 0

Y+0 > 0

Y > 0

Y+0 > 0 // - 0

Y > 0

x in { 3, -2/5*((5*(Y-45/4)+225/4)^(1/2)-15/2), 2/5*((5*(Y-45/4)+225/4)^(1/2)+15/2) }

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