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

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).