2003 AMC 12A Problems/Problem 19
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
Solution 1
If we take the parabola and reflect it over the x - axis, we have the parabola . Without loss of generality, let us say that the parabola is translated 5 units to the left, and the reflection to the right. Then:
Adding them up produces:
This is a line with slope . Since cannot be (because would be a line) we end up with
Solution 2: less computation
WLOG let the parabola be , and the reflected parabola is thus . We can also assume and Therefore, which is a non-horizontal line .
-MP8148
See Also
2003 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 18 |
Followed by Problem 20 |
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