Find Negative Area of y+4=(x+6)²: Quadratic Function Analysis

Find the negative area of the function

$y+4=(x+6)^2$

To find the negative area of the function $y + 4 = (x + 6)^2$, we need to determine where the function is below the x-axis, i.e., where $y < 0$.

The equation can be rewritten as:

$y = (x + 6)^2 - 4$.

We need to solve the inequality:

$(x + 6)^2 - 4 < 0$.

Adding $4$ to both sides gives:

$(x + 6)^2 < 4$.

Taking the square root gives:

$-2 < x + 6 < 2$.

Subtracting $6$ from all sides results in:

$-8 < x < -4$.

Thus, the interval where the function is below the x-axis is $-8 < x < -4$.

This corresponds to answer choice 3 from the given options.