The graph of $y = - x^{2} + 2 x - 1$

lies entirely below the x-axis.

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lies entirely above the x-axis.

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cuts the x-axis.

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touches the x-axis and lies below it.

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Solution

The correct option is C touches the x-axis and lies below it.
$y = - (x^{2} - 2 x + 1)$
$y = - (x - 1)^{2}$
$y = 0 \Rightarrow x = 1$
$∴$ the curve touches x-axis at $x = 1$ and lies completely below it as y is negative for every x.

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