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Q.
A quadratic function $f ( x )$ satisfies $f ( x ) \geq 0$ for all real $x$. If $f (2)=0$ and $f (4)=12$ then the value of $f (6)$ is
Complex Numbers and Quadratic Equations
Solution:
$ 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$