Question

How does the graph of y= -(2x+6)^2+3 compare to the graph of a parent function

Answer 1

Here the list of the transformations applied to the parent function, and their effect:

1. $x^2 \to (2x)^2=4x^2$. This causes a horizontal compression of factor 4.
2. $(2x)^2 \to (2x+6)^2= 4(x+3)^2$. This causes a horizontal translation, 3 units to the left.
3. $(2x+6)^2 \to -(2x+6)^2$. This causes a reflection about the x axis.
4. $-(2x+6)^2 \to -(2x+6)^2+3$. This causes a vertical translation, 3 units up

So, if you start from the graph of $y=x^2$, you have to compress and translate it horizontally, flip it with respect to the x axis, and finally move it up 3 units.