Question

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 + 2x +1?

Answer 1

For f(x) to be g(x), the equation f(x) would shift left one

Answer 2

graph of g(x) will be translated 1 unit to the left

Explanation:

`g(x) = x^2 + 2x +1`

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

`2 by 2= 1`

`1^2=1`

add and subtract 1

`g(x) = x^2 + 2x +1`

`g(x) =(x^2 + 2x +1)-1+1`

now we factor
`x^2+2x+1= (x+1)(x+1)`

`g(x) =(x+1)(x+1)-1+1`

`g(x) =(x+1)^2`

Now we compare with the graph of
`f(x)= x^2`

In g(x), 1 is added with x

So graph of g(x) will be translated 1 unit to the left