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

( $- \infty$ ,9]

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( $- \infty$ ,-9]

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(5, $\infty$ )

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[5, $\infty$ )

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Solution

The correct option is D
[5, $\infty$ )

$x^{2} - 4 x + 9 =$ $x^{2} - 2 (2) x + 4 - 4 + 9$

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

We know that ${(x - 2)}^{2} \geq 0$

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

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

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

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

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