document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166325>Question 166325</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am very interested in how one would derive a quadratic equation from a physical parabola. I have one that measures 3.5\" from vertex to \"mouth\" and 4.5\" across the \"mouth.\" I plotted it on a graph with a y intercept of 3.5 and x intercepts of 2.25, -2.25. I played with your quadratic solver and a graphing calculator and the closest I was able to come to was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-.691x%5E2%2B3.5=0 ALIGN=MIDDLE  ALT=\"-.691x%5E2%2B3.5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. How could I solve this without using the aforementioned tools?\r<BR>\n" );
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document.write( "Thank you  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122589 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=122589\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Center your parabola at (0,0).<BR>\n" );
document.write( "Then the general equation of the parabola becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2 ALIGN=MIDDLE  ALT=\"y=ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From your measurement, at x=2.25, y=3.5,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2 ALIGN=MIDDLE  ALT=\"y=ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.5=a%282.25%29%5E2 ALIGN=MIDDLE  ALT=\"3.5=a%282.25%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3.5%2F%282.25%29%5E2 ALIGN=MIDDLE  ALT=\"a=3.5%2F%282.25%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3.5%2F5.0625 ALIGN=MIDDLE  ALT=\"a=3.5%2F5.0625\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=0.6914 ALIGN=MIDDLE  ALT=\"a=0.6914\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a is the same, the other constant just scales the graph with regards to the origin. <BR>\n" );
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