Calculate the Ascending Area: Finding Region Above y=-(x+1)²+1

Find the ascending area of the function

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

To solve this problem, we'll employ the following steps:

• Step 1: Identify the function's vertex
• Step 2: Determine the parabola's orientation
• Step 3: Identify the domain where the function is increasing

Let's proceed with the solution:

Step 1: The function $y = -(x+1)^2 + 1$ is in vertex form, where $a = -1$, $h = -1$, and $k = 1$. Hence, the vertex is at $(-1, 1)$.

Step 2: Since $a = -1$, the parabola opens downwards. For a downward-opening parabola, the function increases on the left side of the vertex.

Step 3: The function is increasing for $x$ values less than the vertex's x-coordinate. Therefore, the domain where the function is increasing is $x < -1$.

In conclusion, the interval where the function $y = -(x+1)^2 + 1$ is increasing is $\boldsymbol{ x < -1 }$.