Find y = -x² Transformed: 3 Units Left and 4 Units Up

To solve this problem, the following steps are necessary:

We begin with the original function:

• $y = -x^2$

First, we apply the horizontal shift of 3 units to the left. Moving a graph left involves adding a number to $x$ in the equation. Hence, replace $x$ with $(x + 3)$. This manipulatively affects the original function:

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

Next, we apply the vertical shift of 4 units upward. This involves adding 4 to the function:

$y = -(x + 3)^2 + 4$

Therefore, the equation representing the parabola moved 3 spaces to the left and 4 spaces up is:

$y = -(x + 3)^2 + 4$

Verification against the choices confirms that the correct answer is choice (1):

• $y = -(x + 3)^2 + 4$

This is indeed the equation that results after applying the given transformations to the original function $y = -x^2$.