SOLUTION: What is the vertex of f(x)=3x^2-12x+11? I have tried to follow the example in the text and can not figure it out.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: What is the vertex of f(x)=3x^2-12x+11? I have tried to follow the example in the text and can not figure it out.      Log On


   

Question 328433: What is the vertex of f(x)=3x^2-12x+11? I have tried to follow the example in the text and can not figure it out.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the general formula is ___ f(x) = a (x-h)^2 + k , where (h,k) is the vertex

start by separating the terms and factoring out the 3 ___ f(x) = 3 (x^2-4x) + 11

complete the square by adding half of the x-term coefficient , squared
___ you can't change the overall value of the expression ; so anything you add must also be subtracted

f(x) = 3 (x^2 - 4x + [(-4/2)^2] + 11 - 3[(-4/2)^2]

the term to complete the square is added inside the parentheses which is multiplied by 3
___ so when the quantity is subtracted to maintain the value of the expression , it must also be multiplied by 3

f(x) = 3 (x^2 - 4x + 4) + 11 - 12 = 3 (x - 2)^2 - 1

so the vertex is ___ (2,-1)