Find Decreasing Intervals for the Quadratic Function: y = -(x+7)²

To solve this problem, we will follow these steps:

• Step 1: Identify the vertex of the parabola.
• Step 2: Determine the direction in which the parabola opens.
• Step 3: Use the vertex and opening direction to find the intervals over which the function is increasing or decreasing.
• Step 4: Choose the correct multiple-choice answer based on our findings.

Let's work through these steps:

Step 1: The given function is $y = -(x+7)^2$. The vertex form of a quadratic is $y = a(x-h)^2 + k$. Comparing, we have $h = -7$ and $k = 0$, hence the vertex is at $(-7, 0)$.

Step 2: The coefficient $a = -1$, which is less than zero, implies that the parabola opens downwards.

Step 3: Since the parabola opens downwards, the function is increasing to the left of the vertex and decreasing to the right of the vertex. Hence, it is decreasing on the interval where $x > -7$.

Step 4: The interval where the function is decreasing is $x > -7$, which corresponds to the multiple-choice answer $\text{id="3"}: x > -7$.

Therefore, the solution to the problem is $x > -7$.