What are the coordinates of the vertex for f (x) = x2 + 6x + 13?

If you have

y=ax²+bx+c or

f (x) = ax²+bx+c, then the x value of the vertex is - b / (2a)

so

given that the equation is

f (x) = 1x²+6x+13

-b/2a=-6 / (2*1) = - 6/2=-3

the y value is found by subsituting - 3 for x

f (-3) = (-3) ²+6 (-3) + 13

f (-3) = 9-18+13

f (-3) = 4

the coordainates are (-3,4)