Graham, born in an African-American family in California grew up in Los Angeles. Her talent for throwing events was quickly identified and a sixteen-year-old Graham was runner-up at the 1964 United States Olympic Trials and also third at the nationalAmateur Athletic Union meet. At the age of seventeen she won national titles in both the shot put and discus throw at the USA Outdoor Track and Field Championships. After 1965 she decided to focus mainly on the shot put instead, as it was her best event. She defended her shot put national title in 1966 and claimed her first indoor American title at the USA Indoor Track and Field Championships the following year. Outdoors, she was beaten at the 1967 nationals by Maren Seidler, but still she was selected to represent the United States at the 1967 Pan American Games held in Winnipeg. Still a teenager, Graham claimed her first major international medal – a silver – behind Canada's Nancy McCredie, who had entered as the defending champion. Graham's teenage shot put exploits remained the best of the nation for over two decades, with her national high school record lasting until 1990, when it was bettered by Stephanie Wadsworth. In 1968 Graham aimed to make her first Olympic team, but losses to Seidler at both the Olympic trials event and the national championships meant her younger rival was selected instead. The standard of American women's throwing was some way behind Europeans during the period – Graham's best throws were around fifteen while Margitta Gummel won the Olympic title that year with a world record of. Graham moved around clubs after this period, going from a Los Angeles-based club to the Mill Lions, then the Fresno Elans. This coincided with the best years of her career. She won three straight national titles from 1969 to 1971, upturning Seidler's position as America's top shot putter, and set a championship record mark of. Her best international results followed at the inaugural 1969 Pacific Conference Games in Tokyo she was silver medallist behind Barbara Poulsen of New Zealand. The greatest win of her shot putting career came at the 1971 Pan American Games in Cali, Colombia. There she defeated Cuba's Grecia Hamilton to win the gold medal in a Pan American Games mark of. That same year she achieved her personal record of. Graham's last year of high level competition was in 1972. Aiming yet again for the Olympic team, her perennial rival Maren Seidler emerged the better thrower and defeated her at both the Olympic trials and national championships. Graham retired from the sport thereafter while Seidler ultimately pushing American women's throwing to near European standards – her 1972 national win was the first of a nine-year streak which included in a championship record of in 1979.
