Question

The graphs below have the same shape. What is the equation of the blue graph

Answer 1

C.
`g(x)=(x-2)^2`

Explanation:

Remember the rules for function transformations:

-
`f(x+a)` shifts the function,
`f(x)`,
`a` units to the left

-
`f(x-a)` shifts the function,
`f(x)`,
`a` units to the right

We can infer from the picture that the blue graph is shifted 2 units to the right of the red graph, so we should apply the second rule:

`f(x)=x^2`

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

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

We can conclude that the correct answer is C.
`g(x)=(x-2)^2`