SOLUTION: What is the vertex of the absolute value function f(X)=- the absolute value of X-5 -3, and does it open up, or down?

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Question 1197591: What is the vertex of the absolute value function f(X)=- the absolute value of X-5 -3, and does it open up, or down?
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=-+abs%28x-5%29+-3
compare to f%28x%29=-+a%2Aabs%28x-h%29+%2Bk
you see that h=5 and k=-3, so the vertex is at: (5 ,-3)
since a is negative, it opens down





Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Any linear absolute value function abs%28A%29 opens up; any linear absolute value function -abs%28A%29 opens down. So your function -abs%28x-5%29-3 opens down.

The vertex of any linear absolute value function is when the expression inside the absolute value symbols is equal to 0. So in your example, the vertex is when
x-5 = 0
x = 5

To find the y value at the vertex, evaluate the function when the absolute value part is 0. For your example,
f%285%29=-abs%285-5%29-3=0-3=-3

The vertex is when x=5 and y=-3.

ANSWER: vertex(5,-3); opens down