document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192447>Question 1192447</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help me with the equation of a parabola? Please see the attached picture of the graph. Thank you in advance! \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 #824317 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=824317\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "One form of the equation for a parabola with vertex (h,k) that opens upward is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F%284p%29%29%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=%281%2F%284p%29%29%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "With the equation in that form, p is the directed distance (i.e., might be negative) from the vertex to the focus.<br><BR>\n" );
document.write( "Your graph shows the vertex at (0,2); and it shows that the directed distance from the vertex to the focus is +1.  So p=1 and the equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F%284%29%29%28x%29%5E2%2B2 ALIGN=MIDDLE  ALT=\"y=%281%2F%284%29%29%28x%29%5E2%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "You can use the graph to verify the equation by using x=2 or x=-2 and seeing that for both of those x values the value of y is 3.<br><BR>\n" );
document.write( "Outside the scope of your question, note that 4p=4 is the length of the latus rectum -- the segment that is perpendicular to the axis of the parabola through the focus, with endpoints on the parabola.<br><BR>\n" );
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