We can solve this problem using discriminant.
x^2-4x-12's discriminant is
(-4)^2-4*-12=16+48 which is clearly larger than 0
This means that it crosses over the axes 2 times.
In case you don't know what discriminant is, its in equation ax^2+bx+c
the discriminant is b^2-4ac.
If its positive it has 2 crosses with x axis, if negative then 0 crosses, if 0 then 1 cross.
Hope this helped at least a little bit :D