Answer:
Option C. [tex]y=2(x-2)^2+1[/tex] is the answer.
Step-by-step explanation:
To solve this question we will understand first that what is a vertex form of any equation which describes a function.
If an equation of a parabola in standard form is [tex]y = ax^{2} +bx+c[/tex]
Then It's vertex form will be [tex]y=a(x-h)^{2}+k[/tex] and vertex of the parabola will be (h,K).
Now with the help of this fact we will analyze which equation given in vertex form describes the graph.
Given vertex from the graph is (2,1).
A. [tex]y=2(x-1)^2+3[/tex]
Here vertex is (1,3) which differs from the graph.
B. [tex]y=2(x+2)^2+1[/tex]
Here the vertex is (-2,1) which differs from the graph.
C. [tex]y=2(x-2)^2+1[/tex]
From this equation vertex is (2,1) which matches with the graph.
D. [tex]y=2(x-1)^2+2[/tex]
Here the vertex is (-1,2) again mismatch from the graph.
