Sum of coefficients

Algebra Level 3

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

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

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