I have had MANY people explain to me that if your dead on at 100 yards, and your scope is set at 4.5 zoom then your point of impact will change if you change your zoom to 10x or 14x. is that true? If it wont at 100 yards, then what if you shoot a X ring group at 500 yards with your scope set at 10x. then crank your scope up to 14x and shoot another group. will that change your POI?
That's probably not as big an issue as it used to be, but you should check and verify that your particular scope isn't tracking with power changes. It used to be fairly common, but scopes have come a long ways since then.
It's easy enough to check. Just adjust your scope for the appropriate range and center it on a target at that distance with the rifle sitting on a solid rest. Adjust out the parallax with the objective focus. Then carefully zoom the scope and look for any shift between the target and the reticle. Repeat to be sure any movement is caused by the zoom and not by rifle movement. If zooming does not cause relative movement of the image relative to the reticle then it's not affecting POI. If there is relative motion between the reticle and the target image then it must affect POI. If the reticle is located AFTER the zoom mechanism then there is potential for the POI to be affected. How well the scope is designed and constructed will determine if it actually takes place.
Obviously if you're using a second focal plane reticle for hold offs using reticle markings as the reference you will get large POI errors as you change the magnification. That will also happen if a second focal plane reticle isn't properly centered on the optical axis and you use only the crosshair center. That is not normally an external adjustment.
Parallax error can change with a poorly designed second focal plane reticle following a zoom. Even if the scope is perfectly designed high magnifaction will make the parallax error appear larger. The converse of that is that low magnification may cause you to ignore parallax error which is significant.
I general I prefer fixed magnification scopes, or at least scopes with first focal plane reticles. Variable scopes with second focal plane stadia reticles are just an invitation for errors. Some "ballistic drop compensated" scopes actually rely on the offsets generated by the zoom optics. They work fairly well when matched to the ballistics of specific cartridges but only if they're used as intended. (Leatherwood ART scopes for example).
The bottom like is to know your equipment thoroughly and use it in the way it's designed to be used. Don't assume you're doing it right without target shooting at the ranges you expect to hunt. If you can't hit fixed targets accurately you certainly can't make clean kills on game in the field.