How has the graph of f(x)=-2(x+1)^2-4 been transformed from its parent function?

Answer 1

The original function is reflected over the x-axis, then shifted to the left by 1, and moved down by 4.

Answer 2

So you are working with the vertex for of a quadratic function, which is:

f(x) = a(x - h)^2 + k, where

a negative in front of a is a reflection across the x-axis

a: is a vertical dilation(stretch or compression)- if |a| > 1 its a stretch, if |a| < 1 its a compression

inside the parenthesis (h): horizontal translation- you will want to think opposite with this, + left, - right

k: vertical translation- + up, - down

So in your equation

f(x)=-2(x+1)^2-4

The negative in front: Reflection across x-axis

2: Vertical dilation(stretch) by a factor of 2

inside the parenthesis: + 1: left 1 unit

-4: Down 4 units

Hope this helped!