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)?

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- May 8th 2012, 01:32 PMjonathanraxafunction min and 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)?

Thanks - May 8th 2012, 01:48 PMemakarovRe: function min and vertex
What do you know about how the operations $\displaystyle f(x)\mapsto f(x+c)$ and $\displaystyle f(x)\mapsto f(x)+x$ change the graph of f(x)? What are your difficulties in applying this knowledge to this problem?

- May 8th 2012, 02:02 PMjonathanraxaRe: function min and vertex
I'm not sure if I'm understanding the problem correctly. I know there's a way of getting the vertex, but I'm just not sure whether or not I'm missing something else.

- May 8th 2012, 02:12 PMemakarovRe: function min and vertex
- May 9th 2012, 10:46 AMHallsofIvyRe: function min and vertex
You are

**told**where the vertex of y= f(x) is. Whoever assigned this problem expects you to know that replacing "x" with "x- a" shifts the graph right "a" places and adding "b" to the end of the function (g(x)= f(x)+ b) moves the graph up "b" places. - May 9th 2012, 10:44 PMChukaRe: function min and vertex
- May 10th 2012, 02:35 AMemakarovRe: function min and vertex