A "quartic polynomial" is one with highest power "4". That means it can be written as . To determine that polynomial you need to find the values of the 5 coefficients, a, b, c, d, and e. Replace x and y with any 5 of the (x, y) pairs given (I recommend (-2, 21), (-1, 3), (0, 1), (1, 3), and (2, 21) just because they are simplest).

(Noticing that this is an [b]even[b] function simplifies things a lot!)