Answer:
The answer is A.
Step-by-step explanation:
First, recall the vertex form of a quadratic equation: [tex]f(x)=a(x-h)^2+k[/tex], where [tex]h[/tex] represents the horizontal change and [tex]k[/tex] represents the vertical change.
The original equation is [tex]g(x)=x^2[/tex], or, in other words, [tex]g(x)=1(x-0)^2+0[/tex].
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 [tex]h[/tex] and [tex]k[/tex].
We have:
[tex]f(x)=1(x-(+1))^2+(+3)[/tex]
Or, simplified:
[tex]f(x)=(x-1)^2+3[/tex]
The answer is A.
