Question: Do I have a chance of getting into an Ivy League university if I show them that I have improved tremendously academically from my freshman to senior year? How will low freshman and sophomore grades hurt my Ivy chances?
A "rising record," as admission folks call it, is certainly better than a tumbling one. However, low grades at the start of your high school career can damage Ivy-admission odds. This is largely true because so-so grades in the early years of high school make an impact on a class rank that is usually irreparable. In other words, in most high schools, even straight A's in 11 and 12 won't allow those who didn't start off with a bang to climb to the top of the class. Sad but true.
If you're lucky, your school doesn't rank, so you won't get totally torpedoed by your frosh and soph grades, but, nonetheless, you will be competing against tons of very strong students whose records boast only tip-top grades.
If you're really lucky (and talented and diligent, too), you may have unique strengths, interests, family background, etc., that will spur Ivy admission officials to look beyond your 9th and 10th grade record.
Are there are extenuating circumstances that led to your earlier marks (illness, family problems, etc.)? Sometimes it's appropriate to explain them to colleges. Make sure that you don't pass off minor problems ("My sister played her music too loud") as major ones, but do disclose serious issues, if appropriate.
You can also try the College Confidential Academic Index calculator (it's free at http://www.collegeconfidential.com/academic_index.htm) to see how your "numbers" stack up against those of other Ivy aspirants. (You'll need SAT I scores and three SAT II scores to do it.)
Good luck to you.