Problem:
Amanda Reckonwith draws five circles with radii and . Then for each circle she plots the point , where is its circumference and is its area. Which of the following could be her graph?
Answer Choices:
A.
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B.
C.
D.
E.
Solution:
The circumferences of circles with radii through are and , respectively. Their areas are, respectively, and . The points and are graphed in (). It is the only graph of an increasing quadratic function, called a parabola.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions