Question

The graph of the function $y=(-x+6{)}^2-6$ shown below is reflected across the y-axis. What function is represented by the reflected graph?

• A. $y=(x-6{)}^2-6$
• B. $y=(x+6{)}^2+6$
• C. $y=(x-6{)}^2+6$
• D. $y=(x+6{)}^2-6$

Answer 1

The correct option is D $y=(x+6{)}^2-6$

When the graph of function $y=f\left(x\right)$ is reflected across the y-axis, the resultant graph is represented by the function $y=f(-x)$

The function given is $y=(-x+6{)}^2-6$

So, the graph after reflection is

$y=(-(-x)+6{)}^2-6$

$\therefore y=(x+6{)}^2-6$

So, the answer is option (D).