Question

Find the range of following quadratic expression.
$f\left(x\right)=x^2-4x+6$ $\forall x\in (0,1]$.

• A. $[1,6].$
• B. $[3,5].$
• C. $[2,3].$
• D. $[3,6].$

Answer 1

The correct option is D $[3,6].$

$f\left(x\right)$ $={4x}^2-4x+6=x^2-2\times 2x+4-4+6={(x-2)}^2+2$

Hence minimum value at $x=2$

New graph will be the given one.

Also $f\left(1\right)=1-4+6=3$

$\therefore$ Range of $f\left(x\right)$ by graph is $[3,6].$