Question

How do I find the x-intercepts of the graph of `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 `x^2` 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).`