Problem:
The parabolas and intersect the coordinate axes in exactly four points, and these four points are the vertices of a kite of area 12 . What is ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The -intercepts of the two parabolas are -2 and 4 , respectively,
and in order to intersect the -axis, the first must open upward and the second downward. Because the area of the kite is 12 , the -intercepts of both parabolas must be -2 and 2 . Thus so , and so . Therefore .
The problems on this page are the property of the MAA's American Mathematics Competitions