Will (-2) ^2 and - 2^2 have the same solution? Why or why not?

Honestly this whole lesson in class made no since to me lol

Yes they would be because 2^2 or 2x2 = 4 and - 2^2 or - 2x-2 also equals four because a neg x a neg equals a pos

Given function x^2 is even which means that the sign of variable doesn't affect the outcome.

So these type functions for

x and - x give the same results and they are symmetric with respect to y axis.

This happens because when you have even power you multiply the same integer even times. If the integer is positive it will remain positive (doesn't matter how many times you multiply), If the integer is negative and you multiply it twice (by even number) it becomes positive. As long as you solve this for real values x^2 is always non negative number a. k. a 0 or positive.