What is the connection between the y-intercept and the rule y=x^2-2x-8?

The x-intercepts are the ordered pairs that have values of 0 for the y-values.

Various methods exist:

1) Graphing

2) Quadratic Formula

3) Factoring

Let's factor. The coefficient of the x2 term is 1 so we can look at the constant term, - 8, and find its factors that add up to, 2, the coefficient of the x term.

Factors of - 8:

1 + (-8) = - 7, Does not work

(-1) + 8=7, Does not work

2 + (-4) = - 2, Does not work

(-2) + 4=2, Works because it is 2

0 = (x-2) ⋅ (x+4)

Now set each factor equal to zero.

(x-2) = 0

x=2

(x+4) = 0

x=-4

The x-intercepts are (2,0) and (-4,0).