Hope is the daughter of Elain with a beautiful face bestowed upon her by Eragon. No one will let her forget this second fact, but Hope doesn't believe that Eragon even exists. According to everyone else (including her brother, that Eragon worshipper), Eragon left Alagaësia after killing Galbatorix who had supposedly been ruling over the entire country with his tyrannical dragon for centuries.
Yeah right. Hope doesn't believe a scrap of that tale. How could she? Dragon Riders are so abundant they're like gnats on a pile of manure, and a woman named Nasuada has been ruling for her entire life. It's the elves that teach the new dragon Riders, not some mythical boy from Palancar Valley and his sapphire dragon. However, Hope's life is flipped upside down when she finds a mysterious egg that hatches. For her!
The words of warning given to her by an elvish oracle follow Hope through her life: "Watch out for any red dragons, Hope Elainsdaughter, and the blue ones don't look much better."