convert this quadratic formula from stndard from to vertex form f(x)=3x^2-6x+4

Question

i need to know how to do this ?

Answer 1

Given quadratic function f(x) = 3x^2-6x+4

f(x)  = 3x^2-6x+4

f(x)  = 3(x^2-2x)+4

To complete the squre add (half cooefficient of x )^2 .

f(x)  = 3(x^2-2x+1-1)+4

f(x) = 3(x^2-2x+1)-3+4

f(x) = 3(x-1)^2+1

Now which is in vertex  form.

Standard form of parabola f(x) = a(x-h)^2+k

Where a not equals to 0.

Vertex(h,k) = (1,1), a = 3.