I'm assuming that you mean to find the minimum of a parabola, i.e. the minimum of a function defined as
[tex] f(x) = ax^2+bx+c,\quad a,b,c \in\mathbb{R},\quad a\neq 0[/tex]
To find the minimum of a function, we have to find a point [tex] x_0 [/tex] such that
[tex] f'(x_0) = 0,\quad f''(x_0) > 0 [/tex]
The first derivative is
[tex] f'(x) = 2ax+b \implies f'(x)=0 \iff x = \dfrac{-b}{2a} [/tex]
The second derivative is
[tex] f''(x) = 2a [/tex]
So, a parabola has a minimum only if [tex] a>0 [/tex] (otherwise, the parabola is concave down and it has no lower bound). In that case, the minimum has coordinates
[tex] x = \dfrac{-b}{2a},\quad y = f\left(\dfrac{-b}{2a}\right) = a\left(\dfrac{-b}{2a}\right)^2 + b\left(\dfrac{-b}{2a}\right) + c = \dfrac{4ac-b^2}{4a} [/tex]
