document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120774>Question 120774</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A football is kicked into the air and follows the path defined by h=-2x^2+16x, where x is the time in seconds and h is the height in metres.What is the maximum height reached by the football? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88570 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=88570\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you are familiar with the quadratic formula, then you know that a quadratic equation of<BR>\n" );
document.write( "the generic standard form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "has as its solutions for x the values that are given by:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F%282%2Aa%29+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+-b%2F%282%2Aa%29+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The first term on the right side specifies the axis of symmetry. In other words, the axis<BR>\n" );
document.write( "of symmetry is given by:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+-b%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "{Now to your problem. First recognize that the highest point in the parabolic path of the<BR>\n" );
document.write( "football will occur along the axis of symmetry. So let's first find the axis of symmetry<BR>\n" );
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document.write( "Let h be zero so that your quadratic equation of:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-2x%5E2+%2B+16x+ ALIGN=MIDDLE  ALT=\"h+=+-2x%5E2+%2B+16x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-2x%5E2+%2B+16x ALIGN=MIDDLE  ALT=\"0+=+-2x%5E2+%2B+16x\"   DISABLED_style= \"max-width:90%; height:auto;\" > which, by switching sides further becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2+%2B+16x+=+0 ALIGN=MIDDLE  ALT=\"-2x%5E2+%2B+16x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Comparing this term by term to the generic quadratic standard form you can see that a = -2,<BR>\n" );
document.write( "b = +16, and c = 0. Now you can go to the equation for the axis of symmetry to find the <BR>\n" );
document.write( "value of x for the axis of symmetry by substituting -2 for a and +16 for b to get that<BR>\n" );
document.write( "the equation for the axis of symmetry is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F%282%2Aa%29+=+-%2816%29%2F%282%2A%28-2%29%29+=+-16%2F-4+=+4 ALIGN=MIDDLE  ALT=\"x+=+-b%2F%282%2Aa%29+=+-%2816%29%2F%282%2A%28-2%29%29+=+-16%2F-4+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This tells you that the axis of symmetry is the vertical line through the point  on the x-axis<BR>\n" );
document.write( "where x = +4.  So you can tell that the peak in the flight of the ball will occur when <BR>\n" );
document.write( "x = 4 seconds.<BR>\n" );
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document.write( "Return to your equation for the height of the football and you can find the peak height of<BR>\n" );
document.write( "the ball by substituting 4 for x as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-2x%5E2+%2B+16x+=+-2%284%5E2%29+%2B+16%284%29+=+-2%2816%29+%2B+16%284%29+=+-32+%2B+64+=+32 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This tells you that the maximum height of the football is 32 metres. <BR>\n" );
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document.write( "Hope this helps you to understand one way that this problem can be solved.<BR>\n" );
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document.write( " </SPAN>\n" );
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