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

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 $y = {\left(x + 5\right)}^{2}$ 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 $y = {\left(x + 5\right)}^{2} + 1$ 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 $y = - {\left(x + 5\right)}^{2} + 1$ which takes our previous graph and flips it upside down.

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