{"status": "success", "data": {"description_md": "The graph of $y=f(x)$, where $f(x)$ is a polynomial of degree $3$, contains points $A(2,4)$, $B(3,9)$, and $C(4,16)$. Lines $AB$, $AC$, and $BC$ intersect the graph again at points $D$, $E$, and $F$, respectively, and the sum of the $x$-coordinates of $D$, $E$, and $F$ is $24$. What is $f(0)$?\n\n$\\textbf{(A)}\\ -2 \\qquad \\textbf{(B)}\\ 0 \\qquad \\textbf{(C)}\\ 2 \\qquad \\textbf{(D)}\\ \\frac{24}{5} \\qquad\\textbf{(E)}\\ 8$\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>The graph of  <span class=\"katex--inline\">y=f(x)</span> , where  <span class=\"katex--inline\">f(x)</span>  is a polynomial of degree  <span class=\"katex--inline\">3</span> , contains points  <span class=\"katex--inline\">A(2,4)</span> ,  <span class=\"katex--inline\">B(3,9)</span> , and  <span class=\"katex--inline\">C(4,16)</span> . Lines  <span class=\"katex--inline\">AB</span> ,  <span class=\"katex--inline\">AC</span> , and  <span class=\"katex--inline\">BC</span>  intersect the graph again at points  <span class=\"katex--inline\">D</span> ,  <span class=\"katex--inline\">E</span> , and  <span class=\"katex--inline\">F</span> , respectively, and the sum of the  <span class=\"katex--inline\">x</span> -coordinates of  <span class=\"katex--inline\">D</span> ,  <span class=\"katex--inline\">E</span> , and  <span class=\"katex--inline\">F</span>  is  <span class=\"katex--inline\">24</span> . What is  <span class=\"katex--inline\">f(0)</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ -2 \\qquad \\textbf{(B)}\\ 0 \\qquad \\textbf{(C)}\\ 2 \\qquad \\textbf{(D)}\\ \\frac{24}{5} \\qquad\\textbf{(E)}\\ 8</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": 5, "problem_name": "2017 AMC 12B Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc12B_p24", "prev": "/problem/17_amc12B_p22"}}