Which of the following graphs represent $y = x^{2} - 2 x + 5$ .

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Solution

The correct option is B

Consider the given expression $x^{2} - 2 x + 5$

Comparing with a $x^{2}$ + bx + c = 0, a > 0

$\Rightarrow$ Graph is upward parabola

$D = b^{2} - 4 a c = {(- 2)}^{2} - 4 (1) (5)$
$= 4 - 20 = - 16 < 0$

$\Rightarrow$ Graph doesn’t touch or intersect the $x$ -axis.

Therefore, the graph which correctly represent the given expression is:

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