Answer: See the picture attached.
Step-by-step explanation:
By definition, the Quadratic parent function has the following form:
[tex]y=x^2[/tex]
Its is a parabola with its vertex at the point [tex](0,0)[/tex] (or the origin).
It is important to remember these two transformations for a function:
- When [tex]f(x)-k[/tex], the function is shifted "k" units down.
- When [tex]f(x-k)[/tex], the function is shifted "k" units right.
In this case you have the following function:
[tex]f(x)=(x-1)^2-2[/tex]
You can identify that the graph of this function is obtained by shifting the parent function 1 unit right and 2 units down.
Then, the vertex of this parabola is at this point:
[tex](1,-2)[/tex]
Based on this, you can determine that the graph that represents the given function is the one shown attached.
