Question

Find the axis of symmetry of the parabola shown

• A. $x=1$
• B. $x=2.5$
• C. $x=3$
• D. None of these

Answer 1

The correct option is D None of these

The graph is shown in image

Graphical method--

it is clear from the given image that maxima of the curve at $x=2$

hence equation of axis of symmetry of quadratic equation is $x=2$

Other method--

because graph cut the $X$ axis at two point $x=1,x=3$

hence equation of curve is $y=-(x-1)(x-3)$

$y=-x^2+4x-3$ ..... equ($1$)

now axis of symmetry of quadratic equation is $x=-\frac{b}{2a}$

now comapre equ($1$) with $a{x}^2+bx+x=0$

$a=-1,b=+4,c=-3$

now equation of axis of symmetry is$x=-\frac{4}{2\times -1}$

hence equation of axis of symmetry is $x=2$