Transform y=-x²: Shifting 6 Units Left and 1 Unit Down

To solve this problem, we will apply transformations to the original function:

• Step 1: Horizontal Shift

The function $y = -x^2$ needs to be shifted 6 units to the left. In terms of algebraic manipulation, this means taking $x$ in the function and replacing it with $(x + 6)$. The equation becomes:

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

• Step 2: Vertical Shift

Next, we shift the function 1 unit down. This involves subtracting 1 from the entire expression we obtained from the horizontal shift:

$y = -(x + 6)^2 - 1$

This captures both the horizontal and vertical shifts. Therefore, the resulting function after applying these transformations is:

$y = -(x + 6)^2 - 1$