He never really knew he had a quirk or two for that matter, it was activated when he attacked his childhood friend out of rage, soon a black demon speaks with him showing no threats and also giving him a hero like quirk and another one that was fill...
1 month and 2 weeks into the summer and Izuku had started training with his newly gained quirks with hopes of mastering them enough to get him into you UA, where all the students who want to be top heroes go to, his physique changing a little; much more muscle and his height changing from 5&1/4ft. to 5"8ft.
His training consisted of 10km jog, 100 push-ups and sit ups, eating much more proteins and carbohydrates, then testing out the quirk itself. Izuku had no problems with Full counter after finding out how it worked, he had to make the choice of either using his hands or getting a weapon and decided to master both, practicing his hand to hand combat at a local dojo, all that was left was his weapon of choice and to train with it.
"This pile of garbage should be good for something" Izuku said searching through the trash, then a flash of bright light hit Izuku in the eye towards the left. He walks over to the place, grabbing the object and pulling it out with a lot of strength with the object being stuck and all, taking his time to examine the object before him.
"This should work and the dragon looks cool" Izuku said raising the broken sword to the sky.
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Izuku grabs a piece of trash, throws it into the air and slashing the object in half without the blade touching it.
"Glad I found it, I'm definitely gonna keep this, just needs a sheath to keep it in" Izuku thought with a grin, soon finding a sheath for the sword.
Continuing his training for the day, with someone watching from afar on a dock. Her black hair pulled into a spiky ponytail (Oh the oxymoron) with a bang on the right side of her face,her black eyes, slender but thick figure with a bust and hips flat women would envy on site, sporting a purple shirt with a white outline of an atom in the middle, a black skirt above the knees and a pair of black Adidas shoes with a purple purse to match.
Over the course of the time of his training, she watched and admired his motivational drive to keep on training to go beyond at plus ultra; what really fascinated her was his quirks, but it was the demon quirk she was really interested in. The speed, the strength, the agility and so on were so inhuman (Superhuman way), the flights he took to insane heights, the way he'd throw and chop objects was truly unbelievable, but she could see that he had a limit and that limit seemed to get longer to reach with every week.
"He may need help, yeah, I'll just help him with a few pointers and......." Momo thought as Izuku takes notice of her again and waves at her, literally startling her and causing her to blush a little before waving back.
"She's always here, maybe she's just studying my quirk" Izuku thought going back to training; literally slashing the air a lot, Momo see's his aimless goal and decides to help.
Continuous slashing had Izuku in a different universe, Momo walks up to him and literally almost got her neck slit, but he stops the second it was about to hit her.