# Thread: Vertex!

1. ## Vertex!

The function f(x) = x^2 - 18x + 83 achieves its minimum at (9,2). If g(x) = f(x-4)-3, where is the vertex of g(x)?

This problem is driving me crazy!!!!

Okay so far I've tried to do the shift thing. which I got: (13,-1)
Then I tried to just plug it in as is and squared the equation which got me: (13,-4)

Other answers I've tried: (5,-3) (13,2) (5,5) and so many others lols, on the record it said I've tried 28 times.

Seriously, this seems like the EASIEST problem but I just can't get the right answer, please help.

I won't even get full credit anymore but I realllyyyy want to know HOW to get the answer. Thank you~

2. ## Re: Vertex!

$\displaystyle g(x)=(x-4)^2-18(x-4)+80$

Hence :

$\displaystyle g(x)=x^2-26x+168$

Vertex is given by :

$\displaystyle V\left(\frac{-b}{2a},\frac{-D}{4a}\right)$

where :

$\displaystyle a=1 , b=-26 , c=168 , D =b^2-4ac$

3. ## Re: Vertex!

hmmm, so the answer IS (13,-1)? X-x...Great, now i gotta tell the teacher

[Update]
WOW, fail...the answer IS (13,-1)... BUT turns out I had to put the answer in parentheses...maybe i should delete this thread.

God I want to kill myself T_T;;