Final answer:
The quest that became Matisse's legacy was his innovative blend of sensuality, color, and form, notably demonstrated in his masterpiece 'Bonheur de Vivre' which left a profound impact on modern art and influenced his contemporaries, including Picasso.
Step-by-step explanation:
The quest that ended up being Henri Matisse's legacy was the integration of sensuality, mythology, and vivid color in his artworks, resulting in masterpieces that were celebrated in the art world. Matisse's Bonheur de Vivre (Joy of Life), created in 1905-06, is particularly notable.
This work combined the flowing arabesques and contour lines reflected in nature along with a lush palette, deeply influencing peers like Picasso and cementing Matisse's position as a leader of modern art. Through his oeuvre, Matisse pursued the harmony of figures and landscape, merged the foreground and background in unique ways, and created a dialogue with past masters and contemporaries alike, leaving a lasting impact on the course of 20th-century art.