Simplify the function [tex]y=4x^2-8x+2[/tex] in the following way:
[tex]y=4x^2-8x+2=4x^2-8x+4-4+2=4(x^2-2x+1)-2=4(x-1)^2-2.[/tex]
If you have to translate the graph of the function 3 units lower (down), then
[tex]y=4(x-1)^2-2-3=4(x-1)^2-5.[/tex]
The graph of obtained function opens in the same direction as the graph of the function [tex]y=4(x-1)^2-2.[/tex]
Answer: [tex]y=4(x-1)^2-5.[/tex]
