Formula and derivation of coordinates of parabola vertex

Formula and derivation of coordinates of parabola vertex

Let y = ax ^ 2 + BX + C
y = ax^2+bx+c = a(x+b/2a)^2 + (c-b^2/4a)
So: vertex coordinate x = - B / 2A
When a > 0, a (x + B / 2a) ^ 2 ≥ 0, y minimum: (C-B ^ 2 / 4A)
When a

Limit formula
Find the root x power of LIM (1-1 / x), X tends to be positive infinity
I've been thinking hard for a long time, but I really can't do it. Please help me

lim(x→+∞)(1-1/x)^√x
=lim(x→+∞)[1+(-1/x)]^[(-1/x)*(-x*√x)]
=lim(x→+∞)e^(-1/x*√x）
=e^lim(x→+∞)1/√x
=e^0
=1
Or e ^ [ln (1-1 / x) ^ √ x]
=e^[√x*ln(1-1/x)]
√x*ln(1-1/x)
=Ln (1-1 / x) / (1 / √ x) (Robida's law)
=x/(x-1)*[-(-1/x^2)]/[-1/2*x*√x]
=-1/[(x-1)x^2√x]
=0