Question

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

Answer 1

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.