Solving y=(x-1)² Vertical Shift: Finding the Downward Translation

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information
• Step 2: Recognize the formula for vertical translation
• Step 3: Apply the formula for a downward move
• Step 4: Compare to multiple-choice answers to find a match

Now, let's work through each step:
Step 1: The original equation is $y = (x-1)^2$.
Step 2: A translation "downward" results in the formula $y = (x-1)^2 + k$, with $k = -3$ for moving 3 units downward.
Step 3: Substitute $k = -3$ into the formula to get $y = (x-1)^2 - 3$.
Step 4: Among the choices provided, $y = (x-1)^2 - 3$ matches our formula for the translated equation.

Therefore, the solution to the problem is $y = (x-1)^2 - 3$, corresponding to choice 2.