Question

All possible values of expression $x^2-4x+9$ is

• A. ($-\infty$,9]
• B. ($-\infty$,-9]
• C. (5,$\infty$)
• D. [5,$\infty$)

Answer 1

The correct option is D

[5,$\infty$)

$x^2-4x+9=$ $x^2-2\left(2\right)x+4-4+9$

$=(x-2{)}^2+5$

We know that ${\left(x-2\right)}^2\ge 0$

$(x-2{)}^2+5\ge 5$
(or)

$\infty$ > $(x-2{)}^2+5\ge 5$

$\Rightarrow$ $(x-2{)}^2+5\in [5,\infty )$