SOLUTION: Graph: y=- |x - 2| -3 (it is an absolute value) please explain why you did what you did to get the solution, thanks!

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Question 774563: Graph:
y=- |x - 2| -3
(it is an absolute value) please explain why you did what you did to get the solution, thanks!
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Two conditions occur. x-2%3C0 or x-2%3E=0. A change in slope occurs at x=2. The graph will be two rays.

CONDITION x-2%3C0, which also means x%3C2.
y=-abs%28x-2%29-3=-%282-x%29-3
y=-2%2Bx-3
y=x%2B1, which is a ray with endpoint with x=2. This ray is for x%3C2.

CONDITION x-2%3E=0, which means also x%3E=2.
y=-abs%28x-2%29-3=-%28x-2%29-3
y=-x%2B2-3
y=-x-1, which is a ray with endpoint x=2. This ray is for x%3E=2.

The maximum point is (2, 3).