Question

describe how the graph of the function $y=(x-2)^2 - 1$ is related to the graph of the parent function.
vertical translation: select choice
horizontal translation: select choice
dilation: select choice
reflection: select choice

Explanation:

The parent function of $y=(x-2)^2-1$ is $y=x^2$. For transformations of $y=a(x-h)^2+k$:

1. $k=-1$ means a vertical shift down 1 unit.
2. $h=2$ means a horizontal shift right 2 units.
3. $a=1$, so no dilation (stretching/compressing) occurs.
4. There is no negative sign on $a$ or the input, so no reflection.

Answer:

vertical translation: 1 unit down
horizontal translation: 2 units right
dilation: No dilation
reflection: No reflection