Let $f(x)$ be a quadratic polynomial such that $f(-4) = -22,$ $f(-1)=2$, and $f(2)=-1.$ Let $g(x) = f(x)^{16}.$ Find the sum of the coefficients of the terms in $g(x)$ that have even degree. (For example, the sum of the coefficients of the terms in $-7x^3 + 4x^2 + 10x - 5$ that have even degree is $(4) + (-5) = -1.$)
FORMAT PLEASE!!!! I can't emphasize this enough, but recently people have just been straight pasting problems from other sites, so it becomes unreadable. I'd rather just not attempt a problem that I can't clearly interpret(probably most other people too), so please make sure you're not just c + p ing !