# How do you sketch the graph of #y=-(x+2)^2+2 and describe the transformation?

##### 1 Answer

The transformations are: shift two units to the left (horizontal shift), reflect over the

#### Explanation:

Begin with the graph of the parent function:

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

Now we want to deal with each of the transformations one at a time.

Looking at

That gives us this graph:

graph{(x+2)^2 [-10, 10, -5, 5]}

The vertex moved from

Looking back at our function,

Now the graph looks like:

graph{-(x+2)^2 [-10, 10, -5, 5]}

Finally we want to deal with the +2 at the end of the function. That will take the entire graph and shift it two units up (vertically). This changes the vertex to

Here's the final graph:

graph{-(x+2)^2+2 [-10, 10, -5, 5]}

So the transformations are: shift two units to the left (horizontal shift), reflect over the