Problem:
A parabola with equation is reflected about the -axis. The parabola and its reflection are translated horizontally five units in opposite directions to become the graphs of and , respectively. Which of the following describes the graph of ?
Answer Choices:
A. a parabola tangent to the -axis
B. a parabola not tangent to the -axis
C. a horizontal line
D. a non-horizontal line
E. the graph of a cubic function
Solution:
The original parabola has equation , for some , and , with . The reflected parabola has equation . The translated parabolas have equations
so
Since , the graph is a .
The problems on this page are the property of the MAA's American Mathematics Competitions