I need to write an equation in any form for the quadratic graph

Question

https://imgur.com/OkNkCvh

Answer 1

f(x) = a(x - 2)² + 1 vertex form

f(1) = 0

0 = a(1 - 2)² + 1

0 = 4a + 1

-1 = 4a

-1/4 = a

f(x) = (-1/4)(x - 2)² + 1