Question 970912
y+x^2=-(8x+23) 

y=-x^2-8x-23 = -(x^2+8x+23)

Complete the square  -(x^2+8x +16).  Have added -16 to the equation, have to add 16 to the constant outside, now so -23 +16 =-7

y=-(x+4)^2-7

Let's check this.
y= - {x^2+8x +16)-7    This is -x^2-8x-23, which is what we had.  

a=-1, the coefficient of x.

The vertex x value is -b/2a   = - (-8)/(-2) =-4

THE AXIS OF SYMMETRY IS THE LINE X= -4

If x= -4 y=-7

Vertex form y= a (x-h)^2 +k 
y = -1(x+4)^2 -7


{{{graph (300,300,-10,10,-100,100,-x^2-8x-23)}}}