Sum of coefficients

Algebra Level 3

f(0)=1f(4)f(2)=2f(6)f(4)=3 \begin{array} {rl} f(0) & = 1 \\ f(4) - f(2) & = 2\\ f(6) - f(4) & = 3\\ \end{array}

Given that f(x)f(x) is a quadratic polynomial satisfying the three equations above, what is the value of f(8)? f(8)?

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