Question

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

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

Answer 1

The correct option is D None of these

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

Clearly the equation represents a parabola with vertex $(3,4)$ and axis along $y$ axis.

A parabola is only symmetric about its axis

Comparing with the standard parabola

$X^2=4AY$

whose axis if $X=0$

$\Rightarrow x-3=0x=3$

So the given parabola is symmetric about $x=3$ only

Option $D$ is correct.