Which function in the vertex form is equivalent to f (x) = 4+x2-2x

f (x) = 4x - x² - 2x

Vertex form of a parabola: y = a (x - h) ² + k where (h, k) is the vertex of this parabola

y = a. (x - h) ² + k

y = - 1. (x - h) ² + k

Let's factor:

f (x) = - x² - 2x + 4

f (x) = - (x + 1) ² + 1 + 4

f (x) = - (x + 1) ² + 5

So we don't even need to find the vertex, we can just factor.