Question

F(x) = 3x2 – 12x +1
find the vertex.

Answer 1

(2, -11)

Explanation:

`f(x)=3x^2-12x+1\\\\f(x)=3(x^2-4x)+1\\\\f(x)=3(x^2-2\cdot x\cdot2+2^2-2^2)+1\\\\f(x)=3(\underline{x^2-4x+4}-4)+1\\\\f(x)=3[(x-2)^2-4]+1\\\\f(x)=3(x-2)^2-12+1\\\\f(x)=3(x-2)^2-11`

the vertex form of parabola's equation is: f(x) = a(x - h)² + k with vertex (h,k)

x-h = x-2 ⇒ h = 2

+k = -11 ⇒ k = 11

Answer 2

(2,-11) is the vertex