Question

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

Explanation:

Assuming the problem is to identify the vertex of the parabola \( f(x) = -2(x + 5)^2 - 3 \) (a common problem with this function), here's the solution:

Step1: Recall vertex form of a parabola

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

Step2: Compare with given function

Given \( f(x) = -2(x + 5)^2 - 3 \), we can rewrite \( x + 5 \) as \( x - (-5) \). So comparing with \( a(x - h)^2 + k \), we have \( h = -5 \) and \( k = -3 \).

Answer:

The vertex of the parabola is \((-5, -3)\)