First of all, recall that every parabola can be written as
[tex]y=ax^2+bx+c,\quad a\neq 0, b \in \mathbb{R}, c \in \mathbb{R}[/tex]
If [tex]a>0[/tex], the parabola is concave up (and thus it has a minimum value).
If [tex]a<0[/tex], the parabola is concave down (and thus it has a maximum value).
So, in your case, the parabola in concave up.
The x-coordinate of the minimum can be found using
[tex]x=-\dfrac{b}{2a}=-\dfrac{-1}{1}=1[/tex]
And the y-coordinate will be
[tex]f(1)=\dfrac{1}{2}(1)^2-1-9 = -\dfrac{19}{2}[/tex]
So, the minimum value is -19/2 at x=1.
