Question

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

Explanation:

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

Step 1: Recall the vertex form of a parabola

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 is \((-5, -3)\)