Find all real values of a, b, and c such that f(x)-f(x-2)=x?

Let f(x)=ax^2+bx+c be a quadradic function, where a, b and c are parameters.

Find all real values of a, b, and c such that f(x)-f(x-2)=x?
f(x) = ax^2 + bx + c


f(x-2) = a(x-2)^2 + b(x-2) + c


f(x) - f(x-2) = x


ax^2 + bx + c - (a(x-2)^2 + b(x-2) + c) = x


ax^2 + bx + c - (ax^2 - 4ax + 4a + bx - 2b + c) = x


4ax - 4a + 2b = x


equalizing coefficients of x:


4a = 1


a = 1/4


-4a + 2b = 0


b = 2a = 1/2


there's no enough information to find c


c can be any value and the condition f(x) - f(x-2) = x will still hold, therefore


f(x) = (1/4)x^2 + (1/2)x + c
Reply:same here....should have something for you very soon
Reply:f(x)-f(x-2) = ax^2+bx+c - a(x-2)^2-b(x-2)-c=


a·[ 4x-4] + 2b = 4ax-4a+2b = x --%26gt; 4a=1 and -4a+2b=0 --%26gt;


a=1/4 and b=1/2





f(x)=(x^2+2x+4c)/4


for all c in |R





Saludos.

potential break up song