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Nature of Roots

What is the m...

Question

What is the minimum height of any point on the curve $y = x^{2} - 4 x + 6$ above the $x$ -axis?

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Solution

The correct option is D $2$
$y = x^{2} - 4 x + 6$
$= (x - 2)^{2} + 2$
Now $(x - 2)^{2} \geq 0$ for all real $x$ .
Then $(x - 2)^{2} + 2 \geq 2$ for all real $x$ .
Hence, the minimum value of $y$ (or $x^{2} - 4 x + 6$ ) is $2$ , which is the height of the graph above the $x$ -axis.

Suggest Corrections

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