Question

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

• A. $-9$
• B. $-5$
• C. $5$
• D. $9$
• E. $16$

Answer 1

The correct option is A $-9$

For $|16-{(x+5)}^2$ to be minimum, ${(x+5)}^2$ must approach $16$.
Therefore ${(x+5)}^2=16$ , which gives $x+5=\pm 4$ , which implies $x=-1,-9$.
Therefore for $x=-1$ and for $x=-9$ , it will be minimum.
So, the correct answer is option $A$.