since the coefficient of x^2 is positive the parabola will open upwards and we’ll have the minimum value.

thus vertex = \frac{-b}{2a} substituting b = -8 and a = 1

we get x = \frac{8}{2} = 4

putting x = 4 in our equation y=(x-4)^2+2 , we get y =2

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(x - 4)^{2} can never be negative. The rest falls in place.

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Cud u pls add a reference link abt this theory if possible

just goggle maximum/min. value of a quadratic equation and this will be first result:https://www.wikihow.com/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily