SOLUTION: What is the vertex of the graph of y=3|1/2x-3|+6

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Question 806303: What is the vertex of the graph of
y=3|1/2x-3|+6



Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


(6,6) is indeed an element of the solution set of the given equation, but it is certainly not the only one. In fact, there are infinite elements in the solution set for the given equation, so if the answer is given as (6,6), then you must not have shared all the information about this problem.

John

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My calculator said it, I believe it, that settles it
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Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
We get it in the form

y = a|x-h|+k  has vertex (h,k), which is the point at the V.

So we get

y = 3|1%2F2x-3| + 6 in the form y = a|x-h| + k

y = 3|1%2F2x-3| + 6

Factor out 1%2F2 inside the absolute value

y = 3|1%2F2(x-6)| + 6

y = 3·1%2F2|x-6| + 6

y = 3%2F2|x-6| + 6

Compare that to

y = a|x-h| + k  which has vertex (h,k)

a = 3%2F2, h=6, k=6, so the vertex is (6,6)

We get two points, one on each side of the vertex (6,6)

and draw the V-shaped graph

The graph is:



Edwin