Question

Assertion :STATEMENT-$I$ : The curve $y=\frac{-x^2}{2}+x+1$ is symmetric with respect to the line $x=1$. Reason: STATEMENT -2 : A parabola is symmetric about its axis.

• A. Statement -1 is True, Statement -2 is true; Statement-2 is a correct explanation for Statement-1
• B. Statement -1 is True, Statement -2 is true; Statement-2 is NOT a correct explanation for Statement-1
• C. Statement -1 is True, Statement -2 is False
• D. Statement -1 is False, Statement -2 is True

Answer 1

The correct option is A Statement -1 is True, Statement -2 is true; Statement-2 is a correct explanation for Statement-1

$y=-\frac{x^2}{2}+x+1$
$\Rightarrow y=\frac{3}{2}-\frac{1}{2}(x-1{)}^2$
$\Rightarrow$ it is symmetric about $x=1$.
Statement -1 is True, Statement -2 is true; Statement-2 is a correct explanation for Statement-1