2019: two-year-old season

Quadrilateral was ridden in all of her races as a two-year-old by Jason Watson. The filly began her racecourse career in a maiden race over seven furlongs at Newbury Racecourse on 16 August when she started the 7/2 second favourite in a ten-runner field. After racing in mid-division she made steady progress in the last quarter mile, took the lead in the closing stages and won by a neck from the colt Mambo Nights.^[5] Five weeks later, over the same course and distance, Quadrilateral contested a minor fillies' race in which she started the 7/4 second favourite behind the Michael Stoute-trained Melnikova. She was restrained by Watson at the rear of the seven-runner field before moving up to take the lead approaching the final furlong and drawing away from her opponents to win in "impressive" style by eight lengths.^[6]

On 11 October at Newmarket Racecourse Quadrilateral was stepped up is class and started the 9/4 favourite for the Group 1 Fillies' Mile. Her eight opponents included Love (Moyglare Stud Stakes), Cayenne Pepper (Flame Of Tara Stakes), Powerful Breeze (May Hill Stakes), Boomer (Prestige Stakes) and West End Girl (Sweet Solera Stakes). She settled behind the leaders as West End Girl set the pace, before making progress in the last quarter mile. Quadrilateral maintained her run, overtook Powerful Breeze in the final strides and won by a head with a length and a half back to Love in third place.^[7] After the race Charlton said "She kept responding and I thought she did really well to get there. She fought like a good’un and handled the track, it was a great effort really... that was a proper test and she did it 100%."^[8]

2020: three-year-old season

The flat racing season in England was disrupted by the COVID-19 Pandemic and the 1000 Guineas was run a month later than usual on 7 June over the Rowley mile at Newmarket. Quadrilateral headed the betting at odds of 11/4 in a fifteen-runner. With Watson in the saddle she was in contention from the start and kept on well in the closing stages but never looked likely to win and came home third, beaten two and a half quarter lengths and a head by Love and Cloak of Spirits.^[9] Thirteen days later, the filly started favourite for Coronation Stakes at Royal Ascot and finished third behind Alpine Star and Sharing, beaten six lengths by the winner.^[10] On 23 August the filly was dropped in class and started favourite for the Group 3 Atalanta Stakes over one mile at Sandown Park. She raced in second place for most of the way but was unable to make any progress in the closing stages and came home fourth behind the front-running winner Maamora.