Problem Solving (PS) | Given that f(x) = ax^2 + b x + c and f(x + y) = f(x) + f(y) + xy for

Given that\(f(x)=ax^2+bx+c\) and\(f(x+y)=f(x)+f(y)+xy\) for all numbers x and y, where a, b, and c are constants.
If\(a+b+c=3\) , what is the value of\(f(10)\) ?

\( f(x)=ax^2+bx+c\) --> \( f(1)=a+b+c=3\)

\( f(2)= f(1+1)= f(1) +f(1) +1*1= 3+3+1=7\)

\( f(4)= f(2+2)= f(2)+f(2)+ 2*2= 7+7+4=18\)

\( f(8)= f(4+4)= f(4)+ f(4) +4*4= 18+18+16=52\)

\( f(10)= f(8+2)= f(8)+f(2)+ 2*8= 52+7+16= 75\)

The answer isD.
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