What kind of flooring?

Depends on how much of a gap is left after flooring is installed. You may want to use them to cover a noticeable gap between flooring and baseboard. I assume you’re talking about wood floors.

"You may want to use them to cover a noticeable gap between flooring"

Which is why I asked the flooring type. Most require a gap at the wall for expansion which is why the base boards are installed after the flooring.

We are doing laminate flooring

Laminate requires an expansion gap. Go with the quarter round.

I would ask him to take the baseboards off and install it afterwards. I’m no pro, but even I can pry wood off and not splinter it...unless he’s glued it

Yep ^^^, typically 1/2" all the way around the room. And just as an FYI, they should be using a shoe moulding and not quarter round.

Why shoe molding instead?

If your builder is installing your baseboards before your flooring, he must have already installed all of your doors and door jambs.

Any idea how he intends to get the laminate cleanly under the door jambs?

This sounds like a disaster in the making!

Shoe molding has a smaller profile.

I am replacing carpet in my home with laminate and pulling off the baseboards and putting them back at the appropriate height for the flooring. I thought about doing quarter round, but really don't like the look. I would agree with the above poster - have him pull the trim off and replace.

Our baseboards were installed before flooring and we have no quarter round. I massively dislike it

"Shoe molding has a smaller profile."

And the proper profile for the application, Shoe moulding was basically made originally for this application. Comes in both sanitary or ogee as well depending on the base type.

I have installed laminate in many places with no 1/4 round but always with no baseboard in place before install . You need to be picky about how you cut the flooring to leave the minimal gap for expansion and I jut ise a bit thicker basboard . I hate 1/4 round and IMO used for sloppy workmanship like so much cheap trim in homes.

Laminate flooring in my opinion looks better with quarter round. There might be uneven gaps that may appear along the trim and the quarter round will nicely cover it up making it look more finished. Plus it protects your trim. Door casing should be installed before laminate is placed in. Trim can be left off then installed after floor is put in. I just did a trim job where the laminate installer wanted door casing on with no trim. I installed the trim and noticed gaps in some places so a quarter round was definitely needed.

Am puzzled why your contractor/installer installed the baseboard before installing the flooring?

I disagree about installing door casing before flooring. OP says this is a new build. If the jambs and casing are already installed, they will need to use an undercut saw. Very few installers do that well.

If there is a certain look that you wanted and you wrote it in the contract no quarter round, then yes he may have to remove the trim and install thicker trim to offset any gaps showing.