Question

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

Explanation:

Assuming the problem is to analyze the quadratic function \( y = -(x + 1)^2 + 1 \) (e.g., find vertex, direction, etc.):

Step1: Identify vertex form

The vertex form of a quadratic is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. Here, \( y = -1(x - (-1))^2 + 1 \), so \( a = -1 \), \( h = -1 \), \( k = 1 \).

Step2: Determine vertex

From vertex form, vertex is \((h, k) = (-1, 1)\).

Step3: Determine parabola direction

Since \( a = -1 < 0 \), the parabola opens downward.

Answer:

Vertex: \((-1, 1)\), opens downward (or other relevant analysis based on the exact question; if the question was unspecified, this is a common analysis for this quadratic function).