y=-1/16x^2+2x+5

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Solution for y=-1/16x^2+2x+5 equation:


x in (-oo:+oo)

y = (-1/16)*x^2+2*x+5 // - (-1/16)*x^2+2*x+5

y-((-1/16)*x^2)-(2*x)-5 = 0

(1/16)*x^2-2*x+y-5 = 0

1/16*x^2-2*x+y-5 = 0

DELTA = (-2)^2-(1/16*4*(y-5))

DELTA = 4-1/4*(y-5)

4-1/4*(y-5) = 0

4-1/4*(y-5) = 0

21/4-1/4*y = 0

21/4-1/4*y = 0

21/4-1/4*y = 0 // - 21/4

-1/4*y = -21/4 // : -1/4

y = -21/4/(-1/4)

y = 21

DELTA = 0 <=> t_1 = 21

x = 2/(1/16*2) i y = 21

x = 16 i y = 21

( x = ((4-1/4*(y-5))^(1/2)+2)/(1/16*2) or x = (2-(4-1/4*(y-5))^(1/2))/(1/16*2) ) i y > 21

( x = 8*((4-1/4*(y-5))^(1/2)+2) or x = 8*(2-(4-1/4*(y-5))^(1/2)) ) i y > 21

y-21 > 0

y-21 > 0 // + 21

y > 21

x in { 16, 8*((4-1/4*(y-5))^(1/2)+2), 8*(2-(4-1/4*(y-5))^(1/2)) }

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