Me?
y=2(x-5)^2-8
solve the equation for when y=10, show your work algebraically.

Step-by-step explanation:

I've included a graph to confirm the solution.

10 = 2(x - 5)^2 - 8                     Subtract 10 from both sides.

10-10 = 2(x-5)^2 - 8 - 10           Switch

2(X - 5)^2 - 18 = 0                    Divide through by 2

2(x - 5)^2/2  - 18/2 =0

(x - 5)^2 - 9 = 0                        Expand the brackets.

x^2 - 10x + 25 - 9 = 0               Collect like terms

x^2 - 10x + 16  = 0                    Factor

(x - 8)(x - 2) = 0

x = 8

x = 2  

red: 2(x - 5)^2 -8

green: y = 10