SOLUTION: The graph of y=4^x is transformed and the new focal point is (16,7).What is the new function?

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Question 126471: The graph of y=4^x is transformed and the new focal point is (16,7).What is the new function?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The graph of y=4%5Ex is transformed and the new focal point is (16,7).What is the new function?
 
Sorry, but y=4%5Ex does not have a focal point. It looks like this

graph%28300%2C300%2C-3%2C5%2C-3%2C5%2C4%5Ex%29

Did you mean y=4x%5E2? It has this graph

graph%28300%2C300%2C-3%2C20%2C-3%2C20%2C4x%5E2%29

with vertex (0,0) and focal point (0,1)?

If so then the rule is:

To transform the equation of a graph so that
the point (a,b) translates to the new point
(c,d), then replace

x by (x-c+a)

and

y by (y-d+b)

So (a,b) = (0,1) and (c,d) = (16,7)

and we replace

x by (x-c+a) = (x-16+0) = (x-16)

and we replace

y by (y-d+b) = (y-7+1) = (y-6)

replace x by x-16, and y by y-6

y-6=4%28x-16%29%5E2

Then it has this graph

graph%28300%2C300%2C-3%2C20%2C-3%2C20%2C4%28x-16%29%5E2%2B6%29

with focal point (16,7)

Edwin