Question

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

Answer 1

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).