document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1049994>Question 1049994</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Identify the focus, directrix, and axis of symmetry of f(x)=1/16x^2. If possible please add steps. Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #665616 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=665616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You mean for f(x)=(1/16)x^2,  same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%281%2F16%29x%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29=%281%2F16%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?\r<BR>\n" );
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document.write( "The focus and the directrix are the (only slightly) tough parts to solve for.  If you understand parabolas well enough you immediately recognize symmetry axis here is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The basic form of the equation of a parabola with vertical symmetry axis and parabola with vertex as a minimum  AND on the origin is like  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4py=%28x-0%29%5E2%2B0 ALIGN=MIDDLE  ALT=\"4py=%28x-0%29%5E2%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  That is what you would derive using the definition of parabola...   Yes, your function f(x) has its vertex at the origin,  (0,0).\r<BR>\n" );
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document.write( "That equation is more tightly written as  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4py=x%5E2 ALIGN=MIDDLE  ALT=\"4py=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "What does \"p\" mean in that equation?<BR>\n" );
document.write( "<b>p is the distance of the vertex to either the focus or to the directrix</b>.<BR>\n" );
document.write( "Adjust your function to correspond to the form just shown.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%2F1%29%2Af%28x%29=%2816%2F1%29%281%2F16%29x%5E2 ALIGN=MIDDLE  ALT=\"%2816%2F1%29%2Af%28x%29=%2816%2F1%29%281%2F16%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2Af%28x%29=x%5E2 ALIGN=MIDDLE  ALT=\"16%2Af%28x%29=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and compare this to <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%2Ay=x%5E2 ALIGN=MIDDLE  ALT=\"4p%2Ay=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "f(x) clearly means the same as y.\r<BR>\n" );
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document.write( "Noting the corresponding parts,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16=4p ALIGN=MIDDLE  ALT=\"16=4p\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "What is the meaning of p, again?\r<BR>\n" );
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document.write( "Review the Definition of a Parabola and the use and meaning of the terms, Directrix, and Focus; and be sure you understand the Distance Formula.\r<BR>\n" );
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document.write( "One small correction:  The absolute value of p is the distance between the vertex and either to the focus or directrix. </SPAN>\n" );
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