Question

What is the equation of the following graph in vertex form?

Answer 1

The equation is :

y=(x-2)²+1

Answer 2

easy

the equation of a line with vertex (h,k) is
y=a(x-h)²+k

given
vertex is (2,1)
y=a(x-2)²+1

we also know that (0,5) is on the line
x=0 and y=5 is  a solution
5=a(0-2)²+1
5=a(-2)²+1
5=4a+1
minus 1 both sides
4=4a
divide 4
a=1

y=1(x-2)²+1 is the equation
or
y=(x-2)²+1

first option is answer