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For what value of x is |16-(x+5)^(2)| at...

For what value of x is `|16-(x+5)^(2)|` at its minimum ?

A

`-9`

B

`-5`

C

5

D

9

Text Solution

Verified by Experts

The correct Answer is:
A
The absolute value must be at least 0, so the expression must be at ita minimum when it is equal to 0.
`|16-(x+5)^(2)|=0`
`16-(x+5)^(2)=0`
`(x+5)^(2)=16`
`x+5= pm 4`
`x=-9, x=-1`
Of these, only -9 is an answer choice, so (A) is correct.
You can also backsolve fairly easily on this question - plug in each answer choice, and see which gives you the smallest value for the function.
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