document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=331573>Question 331573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please walk me through this.  \r<BR>\n" );
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document.write( "A flare is fired directly upward into the air from a boat that is experiencing engine problems. The height of the flare (in feet) above the water, t seconds after being fired, is given by the formula h  = -16t2 + 96t + 12. If the flare is designed to explode when it reaches its highest point, at what height will this occur?<BR>\n" );
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document.write( "Thank you,<BR>\n" );
document.write( "Jerry<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 #237730 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=237730\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A flare is fired directly upward into the air from a boat that is experiencing engine problems. <BR>\n" );
document.write( "The height of the flare (in feet) above the water, t seconds after being fired,<BR>\n" );
document.write( " is given by the formula h = -16t^2 + 96t + 12.<BR>\n" );
document.write( " If the flare is designed to explode when it reaches its highest point,<BR>\n" );
document.write( " at what height will this occur?<BR>\n" );
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document.write( "h = -16t^2 + 96t + 12 is a parabola, the min/max occurs at the axis of symmetry<BR>\n" );
document.write( "the coefficient of t^2 is negative so is will be a maximum<BR>\n" );
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document.write( "The formula for the axis of symmetry: x = -b/(2a)<BR>\n" );
document.write( "In this equation; x=t; a=-16; b=96;<BR>\n" );
document.write( "we have<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-96%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"%28-96%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-96%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"%28-96%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = +3 secs when max height will occur<BR>\n" );
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document.write( "To find the height substitute 3 sec for t in the original equation<BR>\n" );
document.write( "h = -16(3^2) + 96(3) + 12 <BR>\n" );
document.write( "h = -16(9) + 288 + 12<BR>\n" );
document.write( "h = -144 + 300<BR>\n" );
document.write( "h = 156 ft is max height and occurs in 3 sec<BR>\n" );
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document.write( "Looks like this: h is y axis, t is x axis<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+10%2C+-50%2C+200%2C+-16x%5E2%2B96x%2B12%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+10%2C+-50%2C+200%2C+-16x%5E2%2B96x%2B12%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >    </SPAN>\n" );
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