What you have does not look like Quackgrass to me. There is nothing wrong with a Quackgrass lawn, it looks nice when mowed, is fairly drought tolerant, and can more easily then some of the wimpier turf grasses, crowd out "weeds", and it does not require nearly as much fertilizer as those wimpier turf grasses.
Many sources suggest using a glyphosate product to kill it, but that requires repeated, and expensive treatment, because that does not kill the whole plant and it will grow back as many farmers have learned.

Here is a link that might be useful: Quackgrass

Doom = the "wrong" type of grass in your lawn? Who decided which types of grass you are "supposed" to have?

If this is quackgrass, what do i do Mow it.

You are, of course, welcome to tend your property to your own specifications. Just make sure they really are yours, and not just what somebody else told you they should be.

There is a lawn maintenance forum where you might get some less contentious answers and this question will not likely trip into anyone's pet peeves there. Sorry if I'm wrong and you get more snarky replies that don't answer your question in the way I think you want. I avoid going on that forum so I don't feel the urge to spread my "that's not the only way" views.

Best of luck to you.