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

1 Answer
Anthony R.
Dec 20, 2017

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

Related questions
See all questions in Vertical Shifts of Quadratic Functions
Impact of this question
4383 views around the world
You can reuse this answer
Creative Commons License