document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187647>Question 1187647</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the equation of a parabola with vertex on the line y=2x, axis parallel to the x-axis and passing through (3/2, 1) and (3,4).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818689 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818689\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The given information is unusual, so initially we don't have a good idea of where to go with the problem.  So we do the only thing we can -- write the general form of the equation and use each the two given points in that equation to see what it gives us.<br><BR>\n" );
document.write( "The vertex is on the line y=2x, so we can call the coordinates of the vertex (a,2a).  Then the vertex form of the equation of a parabola parallel to the x-axis with vertex (a,2a) is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-a%29+=+%281%2F%284p%29%29%28y-2a%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-a%29+=+%281%2F%284p%29%29%28y-2a%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Plug in (x,y)=(1.5,1) and (x,y)=(3,4) to get two equations in a and p:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5-a=%281%2F%284p%29%29%281-2a%29%5E2 ALIGN=MIDDLE  ALT=\"1.5-a=%281%2F%284p%29%29%281-2a%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%281.5-a%29=1-4a%2B4a%5E2 ALIGN=MIDDLE  ALT=\"4p%281.5-a%29=1-4a%2B4a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > [1]<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-a=%281%2F%284p%29%29%284-2a%29%5E2 ALIGN=MIDDLE  ALT=\"3-a=%281%2F%284p%29%29%284-2a%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%283-a%29=16-16a%2B4a%5E2 ALIGN=MIDDLE  ALT=\"4p%283-a%29=16-16a%2B4a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > [2]<br><BR>\n" );
document.write( "Subtract [1] from [2]:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%281.5%29=15-12a ALIGN=MIDDLE  ALT=\"4p%281.5%29=15-12a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6p=15-12a ALIGN=MIDDLE  ALT=\"6p=15-12a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2.5-2a ALIGN=MIDDLE  ALT=\"p=2.5-2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p=10-8a ALIGN=MIDDLE  ALT=\"4p=10-8a\"   DISABLED_style= \"max-width:90%; height:auto;\" > [3]<br><BR>\n" );
document.write( "Substitute [3] in [2]:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810-8a%29%283-a%29=16-16a%2B4a%5E2 ALIGN=MIDDLE  ALT=\"%2810-8a%29%283-a%29=16-16a%2B4a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30-34a%2B8a%5E2=16-16a%2B4a%5E2 ALIGN=MIDDLE  ALT=\"30-34a%2B8a%5E2=16-16a%2B4a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%5E2-18a%2B14=0 ALIGN=MIDDLE  ALT=\"4a%5E2-18a%2B14=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5E2-9a%2B7=0 ALIGN=MIDDLE  ALT=\"2a%5E2-9a%2B7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282a-7%29%28a-1%29=0 ALIGN=MIDDLE  ALT=\"%282a-7%29%28a-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3.5 ALIGN=MIDDLE  ALT=\"a=3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "There will be two parabolas that satisfy the given conditions.<br><BR>\n" );
document.write( "(1) a=3.5; 4p=10-8a=-18; 2a=7<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3.5=%28-1%2F18%29%28y-7%29%5E2 ALIGN=MIDDLE  ALT=\"x-3.5=%28-1%2F18%29%28y-7%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(2) a=1; 4p=10-8a=2; 2a=2<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1=%281%2F2%29%28y-2%29%5E2 ALIGN=MIDDLE  ALT=\"x-1=%281%2F2%29%28y-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Here is a graph of the two parabolas, one with vertex (1,2) and the other with vertex (3.5,7) and both passing through the points (1.5,1) and (3,4)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-2%2C6%2C-2%2C10%2Csqrt%282%28x-1%29%29%2B2%2C-sqrt%282%28x-1%29%29%2B2%2Csqrt%28-18%28x-3.5%29%29%2B7%2C-sqrt%28-18%28x-3.5%29%29%2B7%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );