Question

What is the following parabola's axis of symmetry?
$y=(x+3{)}^2+4$

• A. $x=3$
• B. $y=-3$
• C. $x=-3$
• D. $y=3$

Answer 1

The correct option is C $x=-3$

The graph is shown in image

$y=(x+3{)}^2+4$

$y=x^2+6x+13$ .......equ($1$)

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

now on differention w.r.t. $x$

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

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

$0=2ax+b$

hence $x=-\frac{b}{2a}$

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

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

$a=1,b=6,c=13$

now axis of symmetry is $x=\frac{-6}{2\times 1}$

hence axis of symmetry is $x=-3$