An absolute value function with a vertex of (4,14) is negative on the interval (−oo,−2). On what other interval is the function negative?

Alyce Wilkinson 2021-03-11 Answered
An absolute value function with a vertex of (4,14) is negative on the interval (,2).
On what other interval is the function negative?
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Expert Answer

Sadie Eaton
Answered 2021-03-12 Author has 104 answers

Step 1
The absolute value function with vertex (h,k) is defined as f(x)=a |xh|+k.
The vertex is (4,14).
Therefore, f(x)=|x4|+14.
The function can be written without absolute value as f(x)={a(x4)+14x>4a(x4)+14x<4
Step 2
The function is negative on the interval (,2). Since the function is continuous, the value of the function at x=2 will be zero.
Therefore,
a(24)+14=0
a(6)+14=0
6a+14=0
6a=14
a=146
=73
Step 3
Thus, the function becomes f(x)=73|x4|+14.
Find the intervals on which f(x)=73|x4|+14 is negative as follows.
73|x4|+14<0
73|x4|<14
73|x4|>14
373|x4|>143
7|x4|>42
|x4|>6
x4<6 or x4>6
x<6+4 or x>6+4
x<2 or x>10
Step 4
Therefore, the function is negative on the intervalsx<2 and x>10.
That is, the function is negative on (,2)and(10,).
Thus, the other interval in which the function negative is (10,).

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Jeffrey Jordon
Answered 2021-11-11 Author has 2064 answers

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