Answer:
graph of g(x) will be translated 1 unit to the left
Step-by-step explanation:
[tex]g(x) = x^2 + 2x +1[/tex]
LEts write the given g(x) in vertex form
WE apply completing the square method
WE take coefficient of x and then divide it by 2 and then square it
[tex]2 by 2= 1[/tex]
[tex]1^2=1[/tex]
add and subtract 1
[tex]g(x) = x^2 + 2x +1[/tex]
[tex]g(x) =(x^2 + 2x +1)-1+1[/tex]
now we factor [tex]x^2+2x+1= (x+1)(x+1)[/tex]
[tex]g(x) =(x+1)(x+1)-1+1[/tex]
[tex]g(x) =(x+1)^2[/tex]
Now we compare with the graph of [tex]f(x)= x^2[/tex]
In g(x), 1 is added with x
So graph of g(x) will be translated 1 unit to the left