document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1038747>Question 1038747</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I know the answer is y = -16x^2 + 576, but how do I figure out how to write the equation?\r<BR>\n" );
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document.write( "Write the equation of the quadratic function whose graph is a parabola containing the given points.\r<BR>\n" );
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document.write( "An egg is dropped from the top of a 576-foot-high building. The ball is 432 feet above the ground after 3 seconds, and it reaches level ground in 6 seconds. The height above the ground is a quadratic function of the time after the ball is thrown. Write the equation of this function. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #653476 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=653476\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start with the general form of a parabola<BR>\n" );
document.write( "which has a maximum and not a minimum<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+-a%2At%5E2+%2B+b%2At+%2B+c+ ALIGN=MIDDLE  ALT=\"+h+=+-a%2At%5E2+%2B+b%2At+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be positive )<BR>\n" );
document.write( "Each point on the parabola is  ( t,h )<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Since the ball is dropped and not thrown upward,<BR>\n" );
document.write( "The vertex ( peak ) is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5Bv%5D=0+ ALIGN=MIDDLE  ALT=\"+t%5Bv%5D=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The formula for the vertex is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5Bv%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+t%5Bv%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+0+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b=0+ ALIGN=MIDDLE  ALT=\"+b=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "The parabola must have the form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+-a%2At%5E2+%2B+c+ ALIGN=MIDDLE  ALT=\"+h+=+-a%2At%5E2+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "They give you 2 points:<BR>\n" );
document.write( "( 3, 432 )<BR>\n" );
document.write( "( 6, 0 )<BR>\n" );
document.write( "Use these points to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+ ALIGN=MIDDLE  ALT=\"+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+432+=+-a%2A3%5E2+%2B+c+ ALIGN=MIDDLE  ALT=\"+432+=+-a%2A3%5E2+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-9a+%2B+c+=+432+ ALIGN=MIDDLE  ALT=\"+-9a+%2B+c+=+432+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+-a%2A6%5E2+%2B+c+ ALIGN=MIDDLE  ALT=\"+0+=+-a%2A6%5E2+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-36a+%2B+c+=+0+ ALIGN=MIDDLE  ALT=\"+-36a+%2B+c+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Subtract (2) from (1)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-9a+%2B+c+=+432+ ALIGN=MIDDLE  ALT=\"+-9a+%2B+c+=+432+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+36a+-+c+=+0+ ALIGN=MIDDLE  ALT=\"+36a+-+c+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+27a+=+432+ ALIGN=MIDDLE  ALT=\"+27a+=+432+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+16+ ALIGN=MIDDLE  ALT=\"+a+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-36a+%2B+c+=+0+ ALIGN=MIDDLE  ALT=\"+-36a+%2B+c+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-36%2A16+%2B+c+=+0+ ALIGN=MIDDLE  ALT=\"+-36%2A16+%2B+c+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+576+ ALIGN=MIDDLE  ALT=\"+c+=+576+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "So, the equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+-16t%5E2+%2B+576+ ALIGN=MIDDLE  ALT=\"+h+=+-16t%5E2+%2B+576+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Here's the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-1%2C+8%2C+-70%2C+700%2C+-16x%5E2+%2B+576+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-1%2C+8%2C+-70%2C+700%2C+-16x%5E2+%2B+576+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );