document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201101>Question 201101</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the perfect square trinomial whose first two terms are:<BR>\n" );
document.write( "a^2 - 8a\r<BR>\n" );
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document.write( "Solve by completing the square.<BR>\n" );
document.write( "t^2 - 3t - 7 = 0\r<BR>\n" );
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document.write( "An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet<BR>\n" );
document.write( "high. What will be the object's maximum height? When will it attain this 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 #151327 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=151327\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) To find the perfect square trinomial, add the square of half the x-coefficient .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-8a%2B%288%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"a%5E2-8a%2B%288%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a%5E2-8a%2B16+=+%28a-4%29%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28a%5E2-8a%2B16+=+%28a-4%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2) Solve by completing the square:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2-3t-7+=+0 ALIGN=MIDDLE  ALT=\"t%5E2-3t-7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 7 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2-3t+=+7 ALIGN=MIDDLE  ALT=\"t%5E2-3t+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now complete the square in t by adding the square of half the t-coefficient to both sides. This is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F2%29%5E2+=+9%2F4 ALIGN=MIDDLE  ALT=\"%283%2F2%29%5E2+=+9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2-3t%2B9%2F4+=+7%2B%289%2F4%29 ALIGN=MIDDLE  ALT=\"t%5E2-3t%2B9%2F4+=+7%2B%289%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the left side and simplify the right side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t-%283%2F2%29%29%5E2+=+%2828%2F4%29%2B%289%2F4%29 ALIGN=MIDDLE  ALT=\"%28t-%283%2F2%29%29%5E2+=+%2828%2F4%29%2B%289%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t-%283%2F2%29%29%5E2+=+37%2F4 ALIGN=MIDDLE  ALT=\"%28t-%283%2F2%29%29%5E2+=+37%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t-%283%2F2%29+=+%28sqrt%2837%29%29%2F2 ALIGN=MIDDLE  ALT=\"t-%283%2F2%29+=+%28sqrt%2837%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t-%283%2F2%29+=+-%28sqrt%2837%29%29%2F2 ALIGN=MIDDLE  ALT=\"t-%283%2F2%29+=+-%28sqrt%2837%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides of each solution.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28t+=+%283%2Bsqrt%2837%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight_green%28t+=+%283%2Bsqrt%2837%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28t+=+%283-sqrt%2837%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight_green%28t+=+%283-sqrt%2837%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3) Use the formula for the height of an object propelled upward with an initial velocity of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B0%5D ALIGN=MIDDLE  ALT=\"v%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft/sec from an initial height of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B0%5D ALIGN=MIDDLE  ALT=\"h%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=G+=+32+ft%2F%28sec%29%5E2 ALIGN=MIDDLE  ALT=\"G+=+32+ft%2F%28sec%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-%281%2F2%29Gt%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D ALIGN=MIDDLE  ALT=\"h%28t%29+=+-%281%2F2%29Gt%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B0%5D+=+64 ALIGN=MIDDLE  ALT=\"v%5B0%5D+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B0%5D+=+80 ALIGN=MIDDLE  ALT=\"h%5B0%5D+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28h%28t%29+=+-16t%5E2%2B64t%2B80%29 ALIGN=MIDDLE  ALT=\"highlight%28h%28t%29+=+-16t%5E2%2B64t%2B80%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > First find the time t at which the object reaches its maximum height. Remember that this equation, when graphed, will show a parabola that opens downward so that the vertex of the graph will be the maximum point of the curve or the time of maximum height, t.<BR>\n" );
document.write( "The vertex of this parabola is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-b%2F2a ALIGN=MIDDLE  ALT=\"t+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > where a = -16 and b = 64, so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-%2864%29%2F2%28-16%29 ALIGN=MIDDLE  ALT=\"t+=+-%2864%29%2F2%28-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+64%2F32 ALIGN=MIDDLE  ALT=\"t+=+64%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t+=2%29 ALIGN=MIDDLE  ALT=\"highlight%28t+=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >seconds.<BR>\n" );
document.write( "The object will attain its maximum height in 2 seconds. To find the maximum height of the object, subtitute t = 2 into the beginning equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28h%28t%29%29 ALIGN=MIDDLE  ALT=\"highlight%28h%28t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >and solve for h.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%282%29+=+-16%282%29%5E2%2B64%282%29%2B80 ALIGN=MIDDLE  ALT=\"h%282%29+=+-16%282%29%5E2%2B64%282%29%2B80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%282%29+=+-64%2B128%2B80 ALIGN=MIDDLE  ALT=\"h%282%29+=+-64%2B128%2B80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28h%282%29+=+144%29 ALIGN=MIDDLE  ALT=\"highlight%28h%282%29+=+144%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >feet is the maximum height attained by the object.. </SPAN>\n" );
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