STATEMENT-1: The curve y = - x 2 2 + x + 1 is symmetric with respect to the line x = 1 , because STATEMENT-2: A parabola is symmetric about its axis. [2007]

Question

STATEMENT-1: The curve $y = \frac{- x^{2}}{2} + x + 1$ is symmetric with respect to the line $x = 1$ , because

STATEMENT-2: A parabola is symmetric about its axis. [2007]

Smart Achievers · Accepted Answer

(1)

$Given curve is y = - \frac{x^{2}}{2} + x + 1$

$\Rightarrow {(x - 1)}^{2} = - 2 (y - \frac{3}{2}), which is a parabola.$

$It is symmetric with respect to its axis x - 1 = 0$

$∴$ $Both the statements are true and statement-2 is a correct explanation for statement-1.$

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