Question

How do I complete the square of this equation y=x^2-8x+7

Answer 1

Separate the 1st 2 terms from the 3rd term:

y = x^2 - 8x                            + 7
Next, take half of the coefficient of x (that is, half of -8).
  In this case that'd come out to -4.
Square this -4 and add the result (16) to  x^2 - 8x:  x^2 - 8x + 16; subtract -16 from 7:

x^2 - 8x + 16                        7 - 16
Write the trinomial as
a perfect square:

    (x-4)^2                                 -9

The answer is   (x-4)^2 - 9.

This approach is very useful.  Note that the vertex of the parabola represented by the given polynomiql is (4,-9).