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Convexity

The graph of ...

Question

The graph of the equation $y = x^{2} - 4 x + 5$ has its lowest point at

(2, 1)

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(- 2, 1)

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(- 2, - 1)

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(2, - 1)

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Solution

The correct option is A $(2, 1)$
$y = x^{2} - 4 x + 5$
$y^{'} = 2 x - 4 = 0$
$x = 2$
lowest point (minima) at $x = 2$
$y = 2 \times 2 - 4 \times 2 + 5$
$= 1$
$(2, 1)$ is the lowest point.

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