document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=669843>Question 669843</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An object is thrown from the origin of a coordinate system with the x-axis along the ground and the y-axis vertical. Its path, or trajectory, is given by the equation y = 400x – 16x2.  \r<BR>\n" );
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document.write( "a.  For what value of x does the object reach maximum height?\r<BR>\n" );
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document.write( "b.  Find the objects maximum height.\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 #416607 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=416607\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y=400x-16x^2\r<BR>\n" );
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document.write( " Where: y = height and x = time. <BR>\n" );
document.write( "The maximum height occurs at the vertex of the parabola whose x-coordinate  is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F2a ALIGN=MIDDLE  ALT=\"-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the quadratic equation ax^2+bx+c.<BR>\n" );
document.write( " a = -16, b = 400, and c = 0. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F2a%29=+-400%2F-32 ALIGN=MIDDLE  ALT=\"-b%2F2a%29=+-400%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=12.6 seconds  The time at maximum height. \r<BR>\n" );
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document.write( "Substitute this value of x into the original equation and solve for y to get the maximum height. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=400x-16x%5E2 ALIGN=MIDDLE  ALT=\"y=400x-16x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=400%2A12.5-16%2812.5%29%5E2 ALIGN=MIDDLE  ALT=\"y=400%2A12.5-16%2812.5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=2500 feet maximum height reached by the object.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-20%2C30%2C-50%2C2800%2Ccircle%2812.5%2C2500%2C0.3%29%2Cgrid%281%29graph%28500%2C500%2C-20%2C30%2C-50%2C2800%2Cy=400x-16x%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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