Question

How do you sketch the graph of `y=-(x+5)^2+1` and describe the transformation?

Answer 1

See explanation

Explanation:

I think it would be best if we approached this by parts:

Begin with the parent function, that is, start with the standard parabola `y=x^2`

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

Next, we can graph `y=(x+5)^2` which is a standard parabola shifted `5` units to the LEFT. That is, take each point and shift it `5` units to the left. The graph now looks like this:

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

Then we move on `y=(x+5)^2+1` which means we take our previous graph and shift it `1` unit UP. The graph is now this:

graph{(x+5)^2 +1[-10, 10, -5, 5]}

Finally, we have `y=-(x+5)^2+1` which takes our previous graph and flips it upside down.

graph{-(x+5)^2 +1[-10, 10, -5, 5]}
This is our final graph