2006 Cyprus MO/Lyceum/Problem 4
Problem
Given the function , Which of the following is correct, about the graph of ?
A. intersects x-axis
B. touches y-axis
C. touches x-axis
D. has minimum point
E. has maximum point
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 with the x-axis (it is tangent to it). is not true; the graph intersects with 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.
See also
2006 Cyprus MO, Lyceum (Problems) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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