Find the equation of the resulting parabola when y= -2x^2+4x+1 is translated -3 units along the x-axis and 2 units along the y-axis.

I know that you are a very nice person because you have already revealed so much about yourself in your profile. Also, you have a nice, friendly smile.

But, when people post questions concerning answering questions about math on this forum without providing what they think the answer is, or how they think they might arrive at the correct answer, most people on this site would think that they are asking them to do their homework for them.

I would suggest looking at the information on the following link first.

https://www.askmehelpdesk.com/math-sciences/announcement-u-b-read-first-expectations-homework-help-board-b-u.html

To shift the graph vertically, then y=f(x)+c. Where c=2

To shift left horizontally, then f(x-c). Where c=-3


To shift your graph 3 units left horizontally and 2 units upward vertically,

\underbrace{-2(x+3)^{2}+4(x+3)+1}_{\text{left horizontal}}+\overbrace{2}^{\text{upward vertical}}

Now, simplify. Then graph them both and see if it's the appropriate shifts. I think it is:) .

See how it's done now?

Hopefully, this will help you with similar problems now.