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The "x intercept" is where y = 0, which is where the curve crosses the x axis.
Solve y = x^2+ 2x- 8 = 0
You can write that as
y = (x+4) (x-2) = 0
There are two places where y = 0. The factored equation tells you where they are.


how would I find the x-intercepts of
y=x^2+2x-8

and

y=x^2-5x-10

thank you, I'm really having trouble getting this.


y = x^2-5x-10 does not factor easily.
If you solve x^2-5x-10 = 0 with the quadratic equation, you get
y = [5 +/- sqrt 65]/2
= +6.531 and -1.531

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