+69 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) with even exponents. (For example, the sum of the coefficients of the terms in -7x^3 + 5x^2 + 10 with even exponents is 5 and 10).
The standard form for quadratic is $ax^2+bx+c=y$
if $f(-4)=-22, a*(-4)^2+b*(-4)+c=-22$
if $f(-1)=2, a*(-1)^2+b*(-1)+c=2$
if $f(2)=-1, a*(2)^2+b*(-1)+c=-1$
we have a system of three equations, after solving (which you can check), i get
$a=-1, b=3, c=6$
$(-x^2+3x+6)^(16)$
here is the polynomial:
