Question

Write the equation of the parabola y=x^2 + 8x - 51

Answer 1

You already have the equation!  If you want it in vertex form, do this:

y = x^2 + 8x + 16 - 16 - 51, or y = x^2 + 8x + 16 -67, or 
                                                 y = (x+4)^2 - 67.  
The vertex is at (-4,67).