For the equation y = x² - 2x - 8 the variables are a=1, b=-2, c=-8

y-intercept (where x = 0):
    y = 1(0)² - 2(0) - 8 = -8

vertex format (completing the square):
    y = x² - 2x + 1 - 8 - 1 => y = (x - 1)² - 9 (vertex is (1, -9))

x-intercept format ("factored"):

Find factors of -8 (c) whose sum is -2 (b)

Pairwise factors of -8

Candidate	Factor 1	Factor 2	Sum
1	-1	8	7
2	1	-8	-7
3	-2	4	2
4	2	-4	-2

The candidate highlighted above gives us the factors.
    y = (x - 4)(x + 2) (using zero product property, the x-intercepts are 4 and -2)

Graph the three versions of the highlighted equations (using Desmos.com here) and confirm they are equivalent. ALSO, confirm that the y- and x-intercepts are correct, as well as the vertex: