document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=724015>Question 724015</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with these problems:\r<BR>\n" );
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document.write( "Finding the maximum y-value on the graph of y=f(x). <BR>\n" );
document.write( "My problem is f(x)= -x^2+8x+7\r<BR>\n" );
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document.write( "Using quadratic formula to find any x-intercepts on graph of equation.  My problem is y=x^2+6x-1.\r<BR>\n" );
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document.write( "and \r<BR>\n" );
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document.write( "To solve by completing the square what value should be added to each side of equation with problem x^2+16x=-4.\r<BR>\n" );
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document.write( "Thanking you in advance for your help.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #443540 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=443540\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+-x%5E2%2B8x%2B7 ALIGN=MIDDLE  ALT=\"f%28x%29=+-x%5E2%2B8x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >...here you have parabola with <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;\" >, so parabola is facing  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=downward ALIGN=MIDDLE  ALT=\"downward\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the maximum <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-value ALIGN=MIDDLE  ALT=\"y-value\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the graph will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > coordinate of the vertex\r<BR>\n" );
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document.write( " the equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x+-+h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"y+=+%28x+-+h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > coordinate of the vertex\r<BR>\n" );
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document.write( "so, we need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   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%28x%29=+-x%5E2%2B8x%2B7 ALIGN=MIDDLE  ALT=\"f%28x%29=+-x%5E2%2B8x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >...factor completely\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+-x%5E2%2B8x%2B7 ALIGN=MIDDLE  ALT=\"f%28x%29=+-x%5E2%2B8x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >...replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16%2B23 ALIGN=MIDDLE  ALT=\"-16%2B23\"   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%28x%29=-x%5E2%2B8x-16%2B23 ALIGN=MIDDLE  ALT=\"f%28x%29=-x%5E2%2B8x-16%2B23\"   DISABLED_style= \"max-width:90%; height:auto;\" >...group first three terms together\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-%28x%5E2-8x%2B16%29%2B23 ALIGN=MIDDLE  ALT=\"f%28x%29=-%28x%5E2-8x%2B16%29%2B23\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x%5E2-8x%2B16%29=-%28x-4%29%5E2 ALIGN=MIDDLE  ALT=\"-%28x%5E2-8x%2B16%29=-%28x-4%29%5E2\"   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%28x%29=-%28x-4%29%5E2%2B23 ALIGN=MIDDLE  ALT=\"f%28x%29=-%28x-4%29%5E2%2B23\"   DISABLED_style= \"max-width:90%; height:auto;\" >...vertex form...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=4 ALIGN=MIDDLE  ALT=\"h=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=23 ALIGN=MIDDLE  ALT=\"k=23\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, vertex is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2C23 ALIGN=MIDDLE  ALT=\"4%2C23\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the maximum <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-value ALIGN=MIDDLE  ALT=\"y-value\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the graph is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=23 ALIGN=MIDDLE  ALT=\"y=23\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "see it on a graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28+600%2C600%2C+-5%2C+10%2C+-10%2C+35%2Ccircle%284%2C23%2C0.1%29%2Clocate%284%2C23-.2%2C%22V%284%2C23%29%22%29%2Cgraph%28+600%2C600%2C+-5%2C+10%2C+-10%2C+35%2C+-x%5E2%2B8x%2B7%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2.\r<BR>\n" );
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document.write( "Using quadratic formula to find any <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-intercepts ALIGN=MIDDLE  ALT=\"x-intercepts\"   DISABLED_style= \"max-width:90%; height:auto;\" > on graph of equation.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=x%5E2%2B6x-1 ALIGN=MIDDLE  ALT=\"+y=x%5E2%2B6x-1\"   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=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...note 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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6 ALIGN=MIDDLE  ALT=\"b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-1 ALIGN=MIDDLE  ALT=\"c=-1\"   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=x+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%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=x+=+%28-6+%2B-+sqrt%28+36%2B4+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+36%2B4+%29%29%2F2+\"   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=x+=+%28-6+%2B-+sqrt%28+40+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+40+%29%29%2F2+\"   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=x+=+%28-6+%2B-+6.3%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+6.3%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6+%2B+6.3%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B+6.3%29%2F2+\"   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=x+=+0.3%2F2+ ALIGN=MIDDLE  ALT=\"x+=+0.3%2F2+\"   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=x+=+0.15+ ALIGN=MIDDLE  ALT=\"x+=+0.15+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6+-6.3%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-6+-6.3%29%2F2+\"   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=x+=+-12.3%2F2+ ALIGN=MIDDLE  ALT=\"x+=+-12.3%2F2+\"   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=x+=+-6.15+ ALIGN=MIDDLE  ALT=\"x+=+-6.15+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-intercepts ALIGN=MIDDLE  ALT=\"x-intercepts\"   DISABLED_style= \"max-width:90%; height:auto;\" > are at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.15 ALIGN=MIDDLE  ALT=\"0.15\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6.15 ALIGN=MIDDLE  ALT=\"-6.15\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "check it on a graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28+600%2C600%2C+-10%2C+5%2C+-10%2C+10%2Ccircle%280.15%2C0%2C0.1%29%2Ccircle%28-6.15%2C0%2C0.1%29%2Cgraph%28+600%2C600%2C+-10%2C+5%2C+-10%2C+10%2C+x%5E2%2B6x-1%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3. complete the square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B16x=-4 ALIGN=MIDDLE  ALT=\"x%5E2%2B16x=-4\"   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=x%5E2%2B16x%2B4=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B16x%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64-60 ALIGN=MIDDLE  ALT=\"64-60\"   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=x%5E2%2B16x%2B64-60=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B16x%2B64-60=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...group first three terms together\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B16x%2B64%29-60=0 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B16x%2B64%29-60=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >....note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B16x%2B64%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B16x%2B64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is square of a sum\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B8%29%5E2-60=0 ALIGN=MIDDLE  ALT=\"%28x%2B8%29%5E2-60=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " \r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );