# 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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