document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980730>Question 980730</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The function f(t) = t2 + 6t &#8722; 20 represents a parabola.\r<BR>\n" );
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document.write( "Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points)\r<BR>\n" );
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document.write( "Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points)\r<BR>\n" );
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document.write( "Part C: Determine the axis of symmetry for f(t). (2 points) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601808 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=601808\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29+=+t%5E2+%2B+6t+-20 ALIGN=MIDDLE  ALT=\"f%28t%29+=+t%5E2+%2B+6t+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Part A: Rewrite the function in vertex form by completing the square.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29+=+%28t%5E2+%2B+6t%2Bb%5E2%29-b%5E2+-20 ALIGN=MIDDLE  ALT=\"f%28t%29+=+%28t%5E2+%2B+6t%2Bb%5E2%29-b%5E2+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >......recall that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2 ALIGN=MIDDLE  ALT=\"a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and compare it to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29+=+t%5E2+%2B+6t+-+20 ALIGN=MIDDLE  ALT=\"f%28t%29+=+t%5E2+%2B+6t+-+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=6 ALIGN=MIDDLE  ALT=\"2ab=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >; so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=6 ALIGN=MIDDLE  ALT=\"2ab=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A1b=6 ALIGN=MIDDLE  ALT=\"2%2A1b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b=6 ALIGN=MIDDLE  ALT=\"2b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3 ALIGN=MIDDLE  ALT=\"b=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "than we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29+=+%28t%5E2+%2B+6t%2B3%5E2%29-3%5E2+-+20 ALIGN=MIDDLE  ALT=\"f%28t%29+=+%28t%5E2+%2B+6t%2B3%5E2%29-3%5E2+-+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29+=+%28t+%2B+3%29%5E2-9+-+20 ALIGN=MIDDLE  ALT=\"f%28t%29+=+%28t+%2B+3%29%5E2-9+-+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29+=+%28t+%2B+3%29%5E2+-29 ALIGN=MIDDLE  ALT=\"f%28t%29+=+%28t+%2B+3%29%5E2+-29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph.\r<BR>\n" );
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document.write( "compare <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29+=+%28t+%2B+3%29%5E2+-29 ALIGN=MIDDLE  ALT=\"f%28t%29+=+%28t+%2B+3%29%5E2+-29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to vertex form of parabola <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-3 ALIGN=MIDDLE  ALT=\"h=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-29 ALIGN=MIDDLE  ALT=\"k=-29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "so, the vertex is at:\r<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-29 ALIGN=MIDDLE  ALT=\"-29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-20%2C+20%2C+-40%2C+40%2C%0D%0Acircle%28-3%2C-29%2C.2%29%2Clocate%28-3%2C-29%2CV%28-3%2C-29%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-20%2C+20%2C+-40%2C+40%2C+%28x+%2B+3%29%5E2+-29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Part C: Determine the axis of symmetry for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29 ALIGN=MIDDLE  ALT=\"f%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Every parabola has an axis of symmetry which is the line that runs down its 'center'. This line divides the graph into two perfect halves.\r<BR>\n" );
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document.write( "In the picture of on the left, the axis of symmetry is the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3 ALIGN=MIDDLE  ALT=\"x+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-20%2C+20%2C+-40%2C+40%2C%0D%0Acircle%28-3%2C-29%2C.2%29%2Clocate%28-3%2C-29%2CV%28-3%2C-29%29%29%2Cline%28-3%2C35%2C-3%2C-35%29%2C%0D%0A+graph%28+600%2C+600%2C+-20%2C+20%2C+-40%2C+40%2C+%28x+%2B+3%29%5E2+-29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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