2006 Cyprus MO/Lyceum/Problem 4
Revision as of 09:46, 27 April 2008 by I like pie (talk | contribs) (Standardized answer choices; minor edits to solution)
Problem
Given the function , Which of the following is correct, about the graph of ?
Solution
Notice that if , then has the unique root of , so it touches the x-axis, .
From above, is not correct because the graph does not intersect the x-axis (it is tangent to it).
is not true; the graph intersects the y-axis since the parabola opens up or down.
and depend upon the value of ; if , then the parabola has a minimum, and if then the parabola has a maximum.
Thus, the answer is .
See also
2006 Cyprus MO, Lyceum (Problems) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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