quadratic

We  have a parabola  that turns upward....the  min is  found to be  the  y coordinate of the vertex

In the form y= ax^2 + bx + c ,   the x coordinate of  the  vertex =  -b/ (2a)  =   -8 /( 2 * 3)  = -8/ 6=  -4/3

The minimum is

3 ( -4/3)^2  + 8(-4/3)  + 9   =

3 ( 16/9)  - 32/3  +9  =

16/3  - 32/3  + 27/3  =

11 / 3