Locate the vertex of y=3x^2-x+3.

To find out where it is located the vertex of the parable
y, we'll have to establish the quadrant where the coordinates of the vertex of the graph
of y are located.

We know that the coordinates of the
parabola vertex are:

 V(-b/2a;-delta/4a), where a,b,c are
the coefficients of the  function and delta=b^2
-4*a*c.

y=f(x)=3x^2-  x +
3

We'll identify the
coefficients:

a=3, b=-1, c=3, 2a=6,
4a=12

delta=(-1)^2
-4*3*3=1-36=-35

V(-b/2a;-delta/4a)=V(-(-1)/6;-(-35)/12)

V(-(-1)/6;-(-35)/12)
= V(1/6 ; 35/12)

Because the coordinates are both positive,
the vertex is located in the first quadrant: V(1/6 ; 35/12).