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).

Feezbio201902 Mar 3, 2021

#1**+2 **

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:

Guest Mar 3, 2021

edited by
Guest
Mar 3, 2021

edited by Guest Mar 3, 2021

edited by Guest Mar 3, 2021