Question

1. f(x) = -2(x + 5)^2 - 3

Explanation:

Assuming the problem is to analyze the quadratic function \( f(x) = -2(x + 5)^2 - 3 \) (e.g., find vertex, direction of opening, etc.):

Step1: Recall vertex form of a parabola

The vertex form of a parabola is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex.
For \( f(x) = -2(x + 5)^2 - 3 \), we can rewrite \( (x + 5) \) as \( (x - (-5)) \). So, \( a = -2 \), \( h = -5 \), \( k = -3 \).

Step2: Determine vertex

From the vertex form, the vertex is \((h, k) = (-5, -3)\).

Step3: Determine direction of opening

Since \( a = -2 \) (negative), the parabola opens downward.

(If other aspects like axis of symmetry, etc., are needed, similar steps apply. Axis of symmetry is \( x = h = -5 \).)

Answer:

• Vertex: \((-5, -3)\)
• Direction of opening: Downward
• Axis of symmetry: \( x = -5 \) (if applicable)