to find the coordinates of the vertex, you use the formula x=-b/(2a)
in this case, a is 6, b is 5
x=-5/12
Next, find out the value of y when x is -5/12
y= 6(-5/12)^2 +5(-5/12) -6
y=-23/8
so the vertex is at (-5/12, -23/8)
Please double check the calculation by yourself