{"status": "success", "data": {"description_md": "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 $y=(f+g)(x)$?\n\n$\\textbf{(A)}\\ \\text{a parabola tangent to the }x\\text{-axis}$\n\n$\\textbf{(B)}\\ \\text{a parabola not tangent to the }x\\text{-axis}\\qquad\\textbf{(C)}\\ \\text{a horizontal line}$\n\n$\\textbf{(D)}\\ \\text{a non-horizontal line}\\qquad\\textbf{(E)}\\ \\text{the graph of a cubic function}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>A parabola with equation  <span class=\"katex--inline\">y=ax^2+bx+c</span>  is reflected about the  <span class=\"katex--inline\">x</span> -axis. The parabola and its reflection are translated horizontally five units in opposite directions to become the graphs of  <span class=\"katex--inline\">y=f(x)</span>  and  <span class=\"katex--inline\">y=g(x)</span> , respectively. Which of the following describes the graph of  <span class=\"katex--inline\">y=(f+g)(x)</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\text{a parabola tangent to the }x\\text{-axis}</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(B)}\\ \\text{a parabola not tangent to the }x\\text{-axis}\\qquad\\textbf{(C)}\\ \\text{a horizontal line}</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(D)}\\ \\text{a non-horizontal line}\\qquad\\textbf{(E)}\\ \\text{the graph of a cubic function}</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2003 AMC 12A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc12A_p20", "prev": "/problem/03_amc12A_p18"}}