Question 1032348: the vertex of the parabola represented by f(x)= x squared -4x+3 has coordinates (2, -1). find the coordinates of the vertex of the parabola defined by g(x)= f(x-2). explain how you arrived at your answer. the use of set of axis is optional.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
There are actually three ways to go about this.
First, you can simply use the fact that changing the variable from  to  translates the graph  units (to the right if  , left otherwise). I.e. your new vertex is (4, -1)
Second, you can substitute  for in the definition of ) and then simplify. Then calculate the -coordinate of the new vertex using  and finally calculate ) to get the coordinates of the new vertex.
\ =\ x^2\ -\ 4x\ +\ 3)
\ =\ f(x\ -\ 2)\ =\ (x\ -\ 2)^2\ -\ 4(x\ -\ 2)\ +\ 3)
\ =\ x^2\ -\ 8x\ +\ 3)
\ =\ (4)^2\ -\ 8(4)\ +\ 3\ =\ -1)
New vertex: (4,-1)
Third, you can complete the square:
\ =\ (x^2\ -\ 4x\ +\ 4)\ +\ 3\ -\ 4)
\ =\ (x\ -\ 2)^2\ -\ 1)
So, by inspection, the original vertex is, indeed, (2,-1)
Now, define )
\ =\ f(x\ -\ 2)\ =\ ((x\ -\ 2)\ -2)^2\ -\ 1\ =\ (x\ -\ 4)^2\ -\ 1))
And, again by inspection, the new vertex is (4, -1)
John
My calculator said it, I believe it, that settles it
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