2011 AMC 12A Problems/Problem 18
Contents
[hide]Problem
Suppose that . What is the maximum possible value of ?
Solution 1
Plugging in some values, we see that the graph of the equation is a square bounded by and .
Notice that means the square of the distance from a point to point minus 9. To maximize that value, we need to choose the point in the feasible region farthest from point , which is . Either one, when substituting into the function, yields .
Solution 2
Since the equation is dealing with absolute values, the following could be deduced: ,, , and . Simplifying would give , , , and . In , we care most about since both and are non-negative. To maximize , though, would have to be -1. Therefore, when and or , the equation evaluates to .
See also
2011 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 17 |
Followed by Problem 19 |
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All AMC 12 Problems and Solutions |
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