document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192394>Question 1192394</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help with this word problem for a quadratic function?\r<BR>\n" );
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document.write( "The height h (in feet) of a water balloon can be modeled by h(x) = -3x^2 + 24x + 11, where x is the horizontal distance (in feet) from the launch pad. <BR>\n" );
document.write( "The launchpad is adjusted so that the water balloon lands exactly 9 feet away from the launchpad. Write a function that models the new path of the water balloon. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824307 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=824307\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The coefficient of x^2 depends on the force of gravity.<br><BR>\n" );
document.write( "The coefficient of x is determined by the initial vertical velocity.<br><BR>\n" );
document.write( "The constant term is determined by the initial height.<br><BR>\n" );
document.write( "When the problem says the launchpad is adjusted, it means we are adjusting the initial height -- we are not changing the force of gravity or the initial velocity.<br><BR>\n" );
document.write( "So we need to find the value of c in the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29=-3x%5E2%2B24x%2Bc ALIGN=MIDDLE  ALT=\"h%28x%29=-3x%5E2%2B24x%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > for which the height is 0 at x=9:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%289%29=-3%289%5E2%29%2B24%289%29%2Bc=-243%2B216%2Bc=0 ALIGN=MIDDLE  ALT=\"h%289%29=-3%289%5E2%29%2B24%289%29%2Bc=-243%2B216%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-27%2Bc=0 ALIGN=MIDDLE  ALT=\"-27%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=27 ALIGN=MIDDLE  ALT=\"c=27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: After the (height of) the launchpad is adjusted, the function that models the path of the water balloon (as a function of the horizontal distance from the launch pad) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29=-3x%5E2%2B24x%2B27 ALIGN=MIDDLE  ALT=\"h%28x%29=-3x%5E2%2B24x%2B27\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( " </SPAN>\n" );
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