Question

A quadratic function $f(x)$ satisfies $f(x)\ge 0$ for all real $x$. If $f(2)=0$ and $f(4)=12$ then the value of $f(6)$ is

• A. 12
• B. 24
• C. 48
• D. 64

Answer 1

Answer: (C)

$f(x)=\lambda (x-2{)}^2;(\lambda >0)$
$f(4)=\lambda (2{)}^2$
$12=4\lambda$
$\therefore \lambda =3$
$\therefore f(x)=3(x-2{)}^2$
$f(6)=3(6-2{)}^2=3\times 16=48$