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<p align="justify"><font face="times new roman,times,serif" size="4"><em>Dado el gráfico de la siguiente parábola: </em></font></p> <p style="text-align: center;"><font face="times new roman,times,serif" size="4"><em>#graf</em></font></p> <p align="justify"><font face="times new roman,times,serif" size="4"><em>Donde la recta de color verde es la directriz de la parábola y la medida del segmento de color rojo es la distancia entre la directriz y el vértice de esta</em></font><font face="times new roman,times,serif" size="4"><em> (cuyo valor es <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#c2«/mi»«/math»</span>)</span></span></em></font><font face="times new roman,times,serif" size="4"><em><span class="nolink"><span class="nolink"></span></span>.</em></font><font face="times new roman,times,serif" size="4"><em> <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></font><font face="times new roman,times,serif" size="4"><em> Además, se muestra el foco de la parábola que tiene como coordenadas <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»F«/mi»«mi»#F1«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span> </span></span></span></span>; por lo tanto, las coordenadas del vértice,</em></font><font face="times new roman,times,serif" size="4"><em> las coordenadas del</em></font><font face="times new roman,times,serif" size="4"><em> foco y la ecuación de la directriz son: </em></font></p>
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<p align="justify"><font face="times new roman,times,serif" size="4"><em>Solución:</em></font></p> <p align="justify"><font face="times new roman,times,serif" size="4"><em>Las ecuaciones que describen a la parábola y sus elementos son:</em></font></p> <ul> <li> <div align="justify"><font face="times new roman,times,serif" size="4"><em>Parábola con eje focal paralelo al eje <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»Y«/mi»«/math»</span><br /><br /><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«msup»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mi»h«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»=«/mo»«mn»4«/mn»«mi»c«/mi»«mfenced»«mrow»«mi»y«/mi»«mo»-«/mo»«mi»k«/mi»«/mrow»«/mfenced»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />si <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»c«/mi»«mo»§gt;«/mo»«mn»0«/mn»«mo»§nbsp;«/mo»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»y«/mi»«mo»§#10878;«/mo»«mi»k«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span> entonces, la parábola se abre hacia arriba y, si <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»c«/mi»«mo»§lt;«/mo»«mn»0«/mn»«mo»§nbsp;«/mo»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»y«/mi»«mo»§#8804;«/mo»«mi»k«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span> </span></span></span></span></span></span></span></span></span></span></span></span></span>, entonces, la parábola se abre hacia abajo.</em></font></div></li><br /> <li> <div align="justify"><font face="times new roman,times,serif" size="4"><em>Vértice: <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»V«/mi»«mfenced»«mrow»«mi»h«/mi»«mo»,«/mo»«mi»k«/mi»«/mrow»«/mfenced»«/math»</span></span></span></span></span></span></span></span></span></span></span></em></font></div></li> <li> <div align="justify"><font face="times new roman,times,serif" size="4"><em>Foco: <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»F«/mi»«mfenced»«mrow»«mi»h«/mi»«mo»,«/mo»«mi»k«/mi»«mo»+«/mo»«mi»c«/mi»«/mrow»«/mfenced»«/math»</span></span></span></span></span></span> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></font></div></li> <li> <div align="justify"><font face="times new roman,times,serif" size="4"><em>Directriz: <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»L«/mi»«mo»:«/mo»«mo»§nbsp;«/mo»«mi»y«/mi»«mo»=«/mo»«mi»k«/mi»«mo»-«/mo»«mi»c«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></font></div></li> <li> <div align="justify"><font face="times new roman,times,serif" size="4"><em>Parábola con eje focal paralelo al eje <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»X«/mi»«/math»</span><br /><br /><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«msup»«mfenced»«mrow»«mi»y«/mi»«mo»-«/mo»«mi»k«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»=«/mo»«mn»4«/mn»«mi»c«/mi»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mi»h«/mi»«/mrow»«/mfenced»«/math»</span></span></span></span></span></span></span></span></span></span></span> </span></span></span></span></span></span></span></span></span></span></span></span></span><br />si <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»c«/mi»«mo»§gt;«/mo»«mn»0«/mn»«mo»§nbsp;«/mo»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»x«/mi»«mo»§#10878;«/mo»«mi»h«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span> entonces, la parábola se abre hacia la derecha y si <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»c«/mi»«mo»§lt;«/mo»«mn»0«/mn»«mo»§nbsp;«/mo»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»x«/mi»«mo»§#8804;«/mo»«mi»h«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>, entonces la parábola se abre hacia la izquierda. <br /></em></font></div></li><br /> <li> <div align="justify"><font face="times new roman,times,serif" size="4"><em>Vértice: <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»V«/mi»«mfenced»«mrow»«mi»h«/mi»«mo»,«/mo»«mi»k«/mi»«/mrow»«/mfenced»«/math»</span>.</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></font></div></li> <li> <div align="justify"><font face="times new roman,times,serif" size="4"><em>Foco: <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»F«/mi»«mfenced»«mrow»«mi»h«/mi»«mo»+«/mo»«mi»c«/mi»«mo»,«/mo»«mi»k«/mi»«/mrow»«/mfenced»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>.</em></font></div></li> <li> <div align="justify"><font face="times new roman,times,serif" size="4"><em>Directriz: <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»L«/mi»«mo»:«/mo»«mo»§nbsp;«/mo»«mi»x«/mi»«mo»=«/mo»«mi»h«/mi»«mo»-«/mo»«mi»c«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></font></div></li> </ul> <blockquote style="margin-right: 0px;" dir="ltr"> <p align="justify"><font face="times new roman,times,serif" size="4"><em>En este caso, la parábola se abre hacia <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#d5«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span>, luego tenemos que </em></font></p> <p align="justify"><font face="times new roman,times,serif" size="4"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»c«/mi»«mo»=«/mo»«mi»#c1«/mi»«/math»</span></span></span></span></span></span> </span></span></span></span></span></span></span></span></span></span></span></span>, </em></font></p> <p align="justify"><font face="times new roman,times,serif" size="4"><em>la coordenada <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»x«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span> del foco es:<br /></em></font></p> <p align="justify"><font face="times new roman,times,serif" size="4"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#d6«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></font></p> <p align="justify"><font face="times new roman,times,serif" size="4"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"></span></span></span></span></span>y la coordenada <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»y«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span> </span></span></span></span></span></span></span></span></span>es:</span></em></font></p> <p align="justify"><font face="times new roman,times,serif" size="4"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#d7«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>.</span></em></font></p> <p align="justify"><font face="times new roman,times,serif" size="4"><em><span class="nolink">Como el foco de esta parábola es <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»F«/mi»«mi»#F1«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span> </span></span>igualando coordenadas tenemos que:<br /><br /><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#Fx«/mi»«mo»=«/mo»«mi»#d9«/mi»«/math»</span> <br /></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></font></p> <p align="justify"><font face="times new roman,times,serif" size="4"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#Fy«/mi»«mo»=«/mo»«mi»#d10«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></font></p> <p align="justify"><font face="times new roman,times,serif" size="4"><em><span class="nolink">Luego, el vértice de la parábola es:</span></em></font></p> <p align="justify"><font face="times new roman,times,serif" size="4"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»V«/mi»«mo»=«/mo»«mi»#center«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>.</span></span></span></em></font></p> <p align="justify"><font face="times new roman,times,serif" size="4"><em><span class="nolink"><span class="nolink"><span class="nolink">Como la parábola es <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#d5«/mi»«/math»</span>, entonces la ecuación de la directriz es <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#d11«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span>, reemplazando los valores de <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»h«/mi»«mo»§nbsp;«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«mi»c«/mi»«/math»</span></span></span></span></span></span></span></span></span></span>, </span></span>tenemos que la ecuación de la directriz es:</span></span></span></em></font></p> <p align="justify"><font face="times new roman,times,serif" size="4"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»L«/mi»«mo»§nbsp;«/mo»«mo»:«/mo»«mo»§nbsp;«/mo»«mi»#d«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></font></p> <p align="justify"><font face="times new roman,times,serif" size="4"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Por lo tanto, la alternativa correcta es:</span></span></span></span></span></em></font></p> <p style="text-align: center;"><font face="times new roman,times,serif" size="4"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#sol«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></font></p></blockquote>
One or multiple answers?
Multiple answers allowed
One answer only
Shuffle the choices?
Number the choices?
a., b., c., ...
A., B., C., ...
1., 2., 3., ...
i., ii., iii., ...
I., II., III., ...
No numbering
WIRIS variables
Algorithm
Choice 1
Answer
#sol
Grade
None
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Feedback
<p></p><font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">¡Excelente!</span></font><br />
Choice 2
Answer
#op1
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
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Feedback
<p style="font-family: times new roman,times,serif; font-style: italic;"><font size="4">Recuerda que la ecuación de la recta que describe a la directriz es:</font></p> <p style="font-family: times new roman,times,serif; font-style: italic;"><font size="4"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#d8«/mi»«/math»</span></span></span></font></p> <p style="font-family: times new roman,times,serif; font-style: italic;"><font size="4">y también, que las coordenadas del vértice son:</font></p> <p style="font-family: times new roman,times,serif; font-style: italic;"><font size="4"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»h«/mi»«mo»=«/mo»«mi»#h1«/mi»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mi»k«/mi»«mo»=«/mo»«mi»#k1«/mi»«/math»</span></span></span>.</font></p>
Choice 3
Answer
#op2
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
25%
20%
16.66667%
14.28571%
12.5%
11.11111%
10%
5%
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Feedback
<p style="font-family: times new roman,times,serif; font-style: italic;"><font size="4">Recuerda que la ecuación de la recta que describe a la directriz es:</font></p> <p style="font-family: times new roman,times,serif; font-style: italic;"><font size="4"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#d8«/mi»«/math»</span></span></span></font></p> <p style="font-family: times new roman,times,serif; font-style: italic;"><font size="4"><span class="nolink">y que el foco de esta parábola es:</span></font></p> <p style="font-family: times new roman,times,serif; font-style: italic;"><font size="4"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»F«/mi»«mo»=«/mo»«mi»#F1«/mi»«/math»</span></span>.</span></font></p>
Choice 4
Answer
#op3
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
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33.33333%
30%
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Feedback
<p style="font-family: times new roman,times,serif; font-style: italic;"><font size="4">Del gráfico, puedes observar que la parábola se abre hacia <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#d5«/mi»«/math»</span> y que, por lo tanto, la ecuación que describe a la directriz es:</font></p> <p style="font-family: times new roman,times,serif; font-style: italic;"><font size="4"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#d8«/mi»«/math»</span>.</span></span></font></p>
Choice 5
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
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Feedback
Choice 6
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
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33.33333%
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Feedback
Choice 7
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
25%
20%
16.66667%
14.28571%
12.5%
11.11111%
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Feedback
Combined feedback
For any correct response
For any partially correct response
Options
Show the number of correct responses once the question has finished
For any incorrect response
Settings for multiple tries
Penalty for each incorrect try
100%
50%
33.33333%
25%
20%
10%
0%
Hint 1
Hint text
Options
Clear incorrect responses
Show the number of correct responses
Hint 2
Hint text
Options
Clear incorrect responses
Show the number of correct responses
Created / last saved
Created
by
Admin User
on
Tuesday, 17 September 2013, 9:51 AM
Last saved
by
Admin User
on
Tuesday, 17 September 2013, 9:51 AM
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