Answer:
The first option, [tex]y=(x-2)^2+1[/tex]
Step-by-step explanation:
Because the graph is showing a quadratic function we need to start by the equation of a quadratic function in its vertex form, which is:
[tex]y=a(x-h)^2+k[/tex], where:
a= is a transformation coefficient
(h,k)=vertex coordinates
Because the vertex is (2,1) then h=2 and k=1, using the vertex form we obtain:
[tex]y=a(x-2)^2+1[/tex]
Now, because we have an extra point (0,5), we can find 'a' as follows:
[tex]5=a(0-2)^2+1[/tex], which can be simplified as:
[tex]5=4a+1[/tex]
[tex]a=(5-1)/4[/tex]
[tex]a=1[/tex]
Then the vertex form of the graph is:
[tex]y=(x-2)^2+1[/tex], which is the first option.
