Question

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

Explanation:

Assuming the problem is to find the vertex of the quadratic function \( f(x) = -2(x + 5)^2 - 3 \), we can use the vertex form of a quadratic function.

Step 1: Recall the vertex form

The vertex form of a quadratic function is \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola.

Step 2: Identify \( h \) and \( k \) from the given function

In the given function \( f(x) = -2(x + 5)^2 - 3 \), we can rewrite \( (x + 5) \) as \( (x - (-5)) \). So comparing with the vertex form \( f(x) = a(x - h)^2 + k \), we have \( h = -5 \) and \( k = -3 \).

Answer:

The vertex of the parabola defined by \( f(x) = -2(x + 5)^2 - 3 \) is \((-5, -3)\).