How to find the x-intercepts and y-intercepts this parabola:   Y= x^2-4  

Expert Answers
lfryerda eNotes educator| Certified Educator

The x-intercept is found by setting y=0 and solving for x.  The y-intercept is found by setting x=0 and solving for y.  Try and remember that when you are finding an intercept, you are always setting the other coordinate to zero.

For this parabola, we can find the y-intercept by setting x=0 and solving for y.  That is, 



Another way of writing the y-intercept is in point form `(0,-4)`.

To find the x-intercept, we need to do a little more work. We set y=0 and solve for x.

`0=x^2-4`   this can be rearranged to solve for x.

`x^2=4`    now take square roots of both sides



This means there are two x-intercepts.  One is at x=2, and the other is at x=-2.  These can also be written in point form `(2,0)` and `(-2,0)`.

jeew-m eNotes educator| Certified Educator



 = (X-2)(X+2)       [since (a^2-b^2)=(a-b)(a+b)


Therefore Y=(X-2)(X+2)   

So if Y=0 then x=2 or x=-2 ;Here the parabola intecept x-axis

If x=0 then Y=-4;Here the parabola intercept y-axis



y intercept= -4