The wood will have very little strength to hold the screws afterwards, you will probably have to be creative with nuts and bolts to actually hold it together afterwards. Or longer screws and a 2x4 in the back.

The best attempt on a repair would be to pick away any loose bits of particle board that prevent perfect mating, then lightly coat both the chipped pieces and the base with a good quality wood glue and mate them together. Wipe off any excess you see when you mate them together, and clamp down on them using a piece of scrap wood to ensure they would stay in place. If it were me, I'd probably use painters tape to ensure they remain in place before I clamped the wood down. Regarding particle board, it doesn't look any dryer than your typical press-wood furniture; the wood glue will do a good job of forming a good bond.
Like the other post says, you might need to get a little creative with the bolts; my bet given how this looks, you might need to secure the bolts and such with some JB Weld on top of doing the repair, joining both the bolts and whatever flanges that those are secured to.

Yeah, this is the downside of chipboard: it's only kinda-repairable at best.

Wood glue + pressure is a good first step. Wipe the edges carefully to minimize seepage out the edges. After it drys you can rub a dark brown crayon around the edges to get wax into any visible seams to hide them.

To reassemble, you'll want to consider if you can use something like T-nuts. Or, as the other poster suggested, something stronger behind that you actually screw into. Consider that if this part was this weak, probably so are any other similar attachment points. So maybe while you're at it you could reinforce other places similarly.

just mount the headboard to the wall. also totally gets rid of that annoying headboard shimmy and banging against the wall when getting your freak on.

I crushed a leg off my fiberboard bedframe a few years ago when i was transporting the pieces for a move. Figured i had nothing to lose by just gluing and clamping. I probably kept the clamps on for 6 months, afraid if i took them off the bed would collapse. 6 years later it's still holding strong. Good luck. If the first attempt doesnt fix it then there are always more options to try again to add more stability!

I just can't visualize it... I need a picture from further away... Wood glue will hold the wood together but not provide much in strength... But and bolt option if possible or oversized washers if you here Bolting into the frame

You might be able to use a joist hanger type thing. They're intended to work through a combination of through-bolting and bearing so that the wood would rest on a little ledge. This is a thing I've done in the past. It's pretty visible, but it'll hold the bed together. Home Depot carries things like this - by the hardware (nails/screws/etc). It's hard to tell what piece is broken, though.

That's particle board. If you still have the pieces, get yourself some wood glue, slather it on then clamp it. Give it a couple days to cure. Reassemble.

Bondo filler works pretty well on wood.

Do not connect the headboard to the frame. Screw the headboard into the wall. If you can't find studs use dry wall anchors. Use a washer behind the head of the screw so you don't screw right through the headboard.

Just butt the frame up against the headboard afterwards.