Question

which best describes the transformation from the graph of $f(x)=x^2$ to the graph of $f(x)=(x-3)^2-1$?○ left 3 units, down 1 unit○ left 3 units, up 1 unit○ right 3 units, down 1 unit○ right 3 units, up 1 unit

Explanation:

Step1: Recall vertex form rules

For $f(x)=(x-h)^2+k$, $h$ shifts horizontally, $k$ shifts vertically.

Step2: Identify $h$ and $k$ values

Given $f(x)=(x-3)^2-1$, so $h=3$, $k=-1$.

Step3: Interpret horizontal shift

$h=3>0$ means shift right 3 units.

Step4: Interpret vertical shift

$k=-1<0$ means shift down 1 unit.

Answer:

right 3 units, down 1 unit