Translate y=-(x-2)²+4: Moving a Quadratic Function 10 Units Down

Which equation represents the function:

$y=-(x-2)^2+4$

moved 10 spaces down?

To solve this problem, we will perform the following steps:

• Step 1: Identify the original function. It is $y = -(x-2)^2 + 4$.
• Step 2: Determine how many units to move the function. According to the problem, we move it 10 spaces down, which means we subtract 10 from the entire function.
• Step 3: Perform the vertical transformation by modifying the constant term. The new function is:

$y = -(x-2)^2 + 4 - 10$.

Step 4: Simplify the resulting expression:

$y = -(x-2)^2 - 6$.

This adjusted equation shows the original parabola moved 10 spaces down.

If we look at the given choices, our result corresponds to choice 3.

Therefore, the equation representing the function moved 10 spaces down is $y = -(x-2)^2 - 6$.