Question 1038677
You should study what is presented here, very closely:
<a href="https://www.youtube.com/watch?v=MD4AiN1Gsmc">Change a quadratic equation from general form to standard form - video</a>


You can directly read the vertex coordinates from the standard form equation.  That gives information for graphing.


Observe that your given equation is equivalent to {{{x^2+4x+8=0}}}, so you should use this as your starting general-form equation.  
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{{{xCoordinateofVertex=-b/(2a)=-4/(2*1)=-2}}}------Actually this is for the function  {{{y=x^2+4x+8}}}.  The vertex occurs at {{{x=-2}}}.


The only realistic graph for {{{x^2+4x+8=0}}} would be TWO points on a single numberline, only if these are real numbers and not containing imaginary parts.  The zeros for your equation are   {{{(-4+- sqrt(16-4*8))/2=(-4+- sqrt(-32))/2=(-4+- 4*sqrt(-2))/2=(-2+- 2*sqrt(-2))=highlight(-2+- 2i*sqrt(2))}}}.


These are NOT real numbers.