How would I solve algebraically to determine that the equation y=(x+2)^2+1 is equivalent to y=(x-2)^2+1? I keep coming up this the wrong thing.

Thanks

These are not equivalent.

y=(x+2)^2+1
=(x^2) + (4x) + 4 + 1
=(x^2) + (4x) + 5.



y=(x-2)^2+1
=(x^2) - (4x) + 4 + 1
=(x^2) - (4x) + 5.

By equivalent I meant that the parabola of y=(x+2)^2+1 is the reflection of y=(x-2)^2+1 which means that it is its inverse, you can look on the graph and know what the equation of the reflected parabola is and you can check it and its right, I'm just having problems solving this as you would flipping the x and y to create an inverse.