Given:
The quadratic function is:
[tex]f(x)=(x+2)^2+1[/tex]
To find:
The graph of the given quadratic function.
Solution:
The vertex form of a quadratic function is:
[tex]f(x)=a(x-h)^2+k[/tex] ...(i)
Where, a is a constant and (h,k) is the vertex of the graph of the quadratic function.
We have,
[tex]f(x)=(x+2)^2+1[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=1[/tex]
[tex]h=-2[/tex]
[tex]k=1[/tex]
Now,
[tex](h,k)=(-2,1)[/tex]
It means the vertex of the graph of the given function is at point (-2,1).
Only in graph C, the vertex of the parabola is at (-2,1).
Therefore, the correct option is C.
