document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1055058>Question 1055058</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the equation of the parabola that has its vertex at the origin and satisfies the given conditions? \r<BR>\n" );
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document.write( "Axis is the x-axis and p=2<BR>\n" );
document.write( "Axis is the x-axis and the parabola passes through the point (4,2)\r<BR>\n" );
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document.write( "Write the equation in standard form.Determine the vertex ,axis and the direction in which each parabola opens\r<BR>\n" );
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document.write( "X^2-x+3y+1=0<BR>\n" );
document.write( "X^2+2x+2y+3=0\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #670446 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=670446\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first two example parts of the question take an equation form,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%28x-h%29=%28y-0%29%5E2 ALIGN=MIDDLE  ALT=\"4p%28x-h%29=%28y-0%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which you would be able to derive if you assumed a given vertex, directrix, focus.  See a video about the derivation or the discussion in your textbook.\r<BR>\n" );
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document.write( "The example for p=2 would give  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%28x-h%29=%28y-0%29%5E2 ALIGN=MIDDLE  ALT=\"8%28x-h%29=%28y-0%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and since you're also given that vertex is the origin, (0,0), the equation becomes simply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x=y%5E2 ALIGN=MIDDLE  ALT=\"8x=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  If you want this in the more typical standard form, then  x=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%281%2F8%29y%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28%281%2F8%29y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The example for the parabola to contain  point (4,2), and axis of symmetry still be x axis, means you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%28x-h%29=%28y-0%29%5E2 ALIGN=MIDDLE  ALT=\"4p%28x-h%29=%28y-0%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  better,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4px=y%5E2 ALIGN=MIDDLE  ALT=\"4px=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >; and you use the given included point to find the value of p.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=%28y%5E2%29%2F%284x%29 ALIGN=MIDDLE  ALT=\"p=%28y%5E2%29%2F%284x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and putting in the coordinates for the point,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=%282%5E2%29%2F%284%2A4%29 ALIGN=MIDDLE  ALT=\"p=%282%5E2%29%2F%284%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=1%2F4 ALIGN=MIDDLE  ALT=\"p=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and this finished equation is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=y%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28x=y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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