Answer:
f(x) = (x - 10)²
Explanation:
the vertex form of a quadratic function is
f(x) = a(x - h)² + k
(h, k ) are the coordinates of the vertex and a is a multiplier
given
f(x) = x² - 20x + 100
use the method of completing the square
add/subtract ( half the coefficient of the x- term)² to x² - 20x
f(x) = x² + 2(- 10)x + 100 - 100 + 100
= (x - 10)² - 100 + 100
= (x - 10)² + 0 ← in vertex form
which can be simplified to
f(x) = (x - 10)² ← a perfect square