Vertical Shift: Finding y=(x-2)² + 3 Through Function Transformation

Choose the equation that corresponds to the function

$y=(x-2)^2$

moved 3 spaces up.

To solve this problem, we need to apply a vertical shift to the function $y = (x-2)^2$.

When a function $y = f(x)$ is shifted vertically by a constant $k$, the new function becomes $y = f(x) + k$. In this problem, we need to shift the function three units up.

Given the original function $y = (x-2)^2$:

• Step 1: Identify the kind of transformation. We aim to move the function 3 spaces up.
• Step 2: Add 3 to the existing equation. This yields $y = (x-2)^2 + 3$.

The updated equation represents the translated parabola after shifting 3 units upwards.

Comparing this result with the given multiple-choice options, the correct corresponding equation is:

$y = (x-2)^2 + 3$.