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2003 AMC 12A Question 19

AMC12 · 2003 AMC 12A

Question 19

A parabola with equation $y = ax^2 + bx + c$ is reflected about the $x$-axis. The parabola and its reflection are translated horizontally five units in opposite directions to become the graphs of $y = f(x)$ and $y = g(x),$ respectively. Which of the following describes the graph of $y = (f + g)(x)?$
  1. a parabola tangent to the $x$-axis
  2. a parabola not tangent to the $x$-axis
  3. a horizontal line
  4. a non-horizontal line
  5. the graph of a cubic function