If f(0) = 0, f(1) = 2, f(2) = 5 , and ax^2+bx+c=0, what is the value of f(3)?
thanks!
+14995 If f(0) = 0, f(1) = 2, f(2) = 5 , and ax^2+bx+c=0, what is the value of f(3)?
Hello Guest!
\(f(x)=ax^2+bx+c\)
\(\color{BrickRed}f(0)=0\\ \color{blue} c=0\)
\(\color{BrickRed}f(1)=2\\ a+b=2 \)
\(\color{BrickRed}f(2)=5\\ 4a+2b=5\)
\(b=2-a\\ 4a+2(2-a)=5\\ 4a+4-2a=5\\ 2a=1 \)
\(a=\frac{1}{2}\\ b=\frac{3}{2}\)
\(f(x)=\frac{1}{2}x^2+\frac{3}{2}x+0\)
\(f(3)=\frac{1}{2}\cdot 3^2+\frac{3}{2}\cdot 3\)
\(f(3)=9\)
!
