Question

Describe the transformations applied to `y=x²` to obtain the graph of `y=-(x+3)²-2`?

Answer 1

`y=x^2`
graph{x^2 [-10, 10, -5, 5]}

`y=(x` `color(red)(+3))^2`
The graph shifts `3` units to the left.
graph{(x+3)^2 [-10, 10, -5, 5]}

`y=color(red)(-)(x+3)^2`
The graph is reflected over the `x`-axis.
graph{-(x+3)^2 [-10, 10, -5, 5]}

`y=-(x+3)^2` `color(red)(-2)`
The graph is shifted `2` units down.
graph{-(x+3)^2-2 [-10, 10, -7, 3]}