from fractions import Fraction
f0, f1, f2 = map(Fraction, (2, 5, 10))
c = f0
a = (f2 - 2 * f1 + f0) / 2
b = f1 - a - c
def f(n):
    return a * n * n + b * n + c
assert [f(n) for n in range(3)] == [f0, f1, f2]
result = {"coefficients": [str(a), str(b), str(c)], "f10": str(f(10)),
          "sum_1_to_10": str(sum(f(n) for n in range(1, 11)))}
import json
print(json.dumps(result, ensure_ascii=False, sort_keys=True))