Question 976585
The fastest solution is to know the equation for vertex:

{{{x=-b/2a}}}

In your equation, a=1, b=4

so

{{{x=-4/2 = -2}}}

now solve for y 

{{{y=(-2)^2+4(-2)+3}}}

{{{y=4-8+3}}}

{{{y=-1}}}


(-2,-1)