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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).

 Mar 3, 2021
edited by Feezbio201902  Mar 3, 2021
 #1
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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: 

 Mar 3, 2021
edited by Guest  Mar 3, 2021
edited by Guest  Mar 3, 2021
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Thanks so much!!!!!!!!!!!!! :)

 Mar 3, 2021
 #3
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I put it in and it is wrong, thanks for help anyway, appreciate it.

 Mar 5, 2021

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