Question

The graph of F(x), shown below, has the same shape as the graph of

G(X) = x2, but it is shifted up 3 units and to the right 1 unit. What is its
equation?

Answer 1

The answer is A.

Explanation:

First, recall the vertex form of a quadratic equation:
`f(x)=a(x-h)^2+k`, where
`h` represents the horizontal change and
`k` represents the vertical change.

The original equation is
`g(x)=x^2`, or, in other words,
`g(x)=1(x-0)^2+0`.

We are told that the graph is shifted up 3 and right 1. Thus, both values are positive (right and up). Note that up 3 corresponds to a positive vertical change of 3 while right 1 represents a positive horizontal change of 1.

Thus, put these back into the equation in place of
`h` and
`k`.

We have:

`f(x)=1(x-(+1))^2+(+3)`

Or, simplified:

`f(x)=(x-1)^2+3`

The answer is A.