document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182891>Question 1182891</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Anatomy of a Parabola in Action \r<BR>\n" );
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document.write( "The height of a diver above water during a dive can be modeled by \r<BR>\n" );
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document.write( "h(t) = -16t^2 + 8t + 20. \r<BR>\n" );
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document.write( "where his height in feet and t is time in seconds. \r<BR>\n" );
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document.write( "5. Find the line of symmetry. \r<BR>\n" );
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document.write( "6. State the meaning of the line of symmetry in terms of the situation. \r<BR>\n" );
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document.write( "7. Find the vertex. \r<BR>\n" );
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document.write( "8. State the meaning of the vertex in terms of the situation. \r<BR>\n" );
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document.write( "9. What is the practical domain? \r<BR>\n" );
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document.write( "10. What is the practical range?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812998 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=812998\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Anatomy of a Parabola in Action<BR>\n" );
document.write( "The height of a diver above water during a dive can be modeled by\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2+%2B+8t+%2B+20 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2+%2B+8t+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > is  his height in feet and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > is time in seconds \r<BR>\n" );
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document.write( "5. Find the line of symmetry.\r<BR>\n" );
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document.write( "recall: parabola’s line of symetry passes through vertex, and it is a line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=a ALIGN=MIDDLE  ALT=\"x=a\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > coordinate of the vertex\r<BR>\n" );
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document.write( "so, write equation in vertex form by completing a square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+%28-16t%5E2+%2B+8t%29+%2B+20 ALIGN=MIDDLE  ALT=\"h%28t%29+=+%28-16t%5E2+%2B+8t%29+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >...factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16 ALIGN=MIDDLE  ALT=\"-16\"   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=h%28t%29+=+-16%28t%5E2+-+t%2F2%29+%2B+20 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16%28t%5E2+-+t%2F2%29+%2B+20\"   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=h%28t%29+=+-16%28t%5E2+-+%281%2F2%29t%2Bb%5E2%29+-%28-16b%5E2%29%2B+20 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16%28t%5E2+-+%281%2F2%29t%2Bb%5E2%29+-%28-16b%5E2%29%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >....since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=%281%2F2%29%2F2=1%2F4 ALIGN=MIDDLE  ALT=\"b=%281%2F2%29%2F2=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16%28t%5E2+-+t%2F2%2B%281%2F4%29%5E2%29+%2B16%281%2F4%29%5E2%2B+20 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16%28t%5E2+-+t%2F2%2B%281%2F4%29%5E2%29+%2B16%281%2F4%29%5E2%2B+20\"   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=h%28t%29+=+-16%28t+-+1%2F4%29%5E2+%2B16%281%2F16%29%2B+20 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16%28t+-+1%2F4%29%5E2+%2B16%281%2F16%29%2B+20\"   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=h%28t%29+=+-16%28t+-+1%2F4%29%5E2+%2B1%2B+20 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16%28t+-+1%2F4%29%5E2+%2B1%2B+20\"   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=h%28t%29+=+-16%28t+-+1%2F4%29%5E2+%2B21 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16%28t+-+1%2F4%29%5E2+%2B21\"   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=h=1%2F4 ALIGN=MIDDLE  ALT=\"h=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=21 ALIGN=MIDDLE  ALT=\"k=21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the line of symmetry is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F16 ALIGN=MIDDLE  ALT=\"x=1%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "6. State the meaning of the line of symmetry in terms of the situation.\r<BR>\n" );
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document.write( "The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. \r<BR>\n" );
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document.write( "7. Find the vertex.\r<BR>\n" );
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document.write( "vertex is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21 ALIGN=MIDDLE  ALT=\"21\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "8. State the meaning of the vertex in terms of the situation.\r<BR>\n" );
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document.write( "The vertex of a parabola is the point where the parabola crosses its axis of symmetry.  In this case,  the vertex will be the highest point on the graph or maximum.\r<BR>\n" );
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document.write( "9. What is the practical domain?\r<BR>\n" );
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document.write( "domain is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > (all real numbers)<BR>\n" );
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document.write( "10. What is the practical range?\r<BR>\n" );
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document.write( "since maximum is at vertex where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29=21 ALIGN=MIDDLE  ALT=\"h%28x%29=21\"   DISABLED_style= \"max-width:90%; height:auto;\" >, range is\r<BR>\n" );
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document.write( "{ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > element<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R ALIGN=MIDDLE  ALT=\"+R\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29%3C=21 ALIGN=MIDDLE  ALT=\"h%28x%29%3C=21\"   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=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+25%2C++-16%28x+-+1%2F4%29%5E2+%2B21%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+25%2C++-16%28x+-+1%2F4%29%5E2+%2B21%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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