Question

What is the following parabola's axis of symmetry?
$y=x^2-4x+5$

• A. $x=-2$
• B. $x=2$
• C. $y=-2$
• D. None of these

Answer 1

Answer: (B)

$x=2$

The graph is shown in the image.

$y=x^2-4x+5$ .......eq($1$)

$a{x}^2+bx+c=0$ .......eq($2$)

On differentiation w.r.t. $x$,

$\frac{dy}{dx}=2ax+b$

Now for maxima, minima and for the axis of symmetry, put $\frac{dy}{dx}=0$

$0=2ax+b$

Hence, $x=-\frac{b}{2a}$

The axis of symmetry of parabola is $x=-\frac{b}{2a}$

Comapare the equ($1$) with $a{x}^2+bx+c$ ,

$a=1,b=-4,c=5$

Now, axis of symmetry is $x=-(\frac{-4}{2\times 1})$

Hence, axis of symmetry is $x=2$.