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

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`y = x^(2) - 4x + 6`
= `(x - 2)^(2) + 2`
Now `(x - 2)^(2) ge 0` for all real x.
Then `(x - 2)^(2) + 2 ge 2` for all real .x
Hence, the maximum value of `y (or - x^(2) + 6x - 5)` is 4 , which is the maximum height of the graph of the graph above x -axis.
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