Calculate the Descending Area of y=(x+4)² : Step-by-Step Guide

Find the descending area of the function

$y=(x+4)^2$

To solve this problem, we will identify and use the vertex of the quadratic function. Knowing that the function $y = (x+4)^2$ is a parabola, we recognize it is in vertex form. The general form of a parabola is $y = (x-h)^2 + k$, hence the vertex of our function is at $(h, k) = (-4, 0)$.

Next, it's important to understand the behavior of the function around this vertex. Since the parabola opens upwards (as can be seen from the positive coefficient of the squared term), it will decrease as $x$ moves towards negative infinity, reach its minimum value at the vertex, and then increase as $x$ becomes larger than the vertex.

Therefore, the function is decreasing on the interval to the left of the vertex. This describes when $x < -4$.

To conclude, the solution to the problem is that the function is decreasing for $x < -4$.