document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103792>Question 103792</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0030565111/algebrahomeworkh>Precalculus A GRAPHING APPROACH</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> My question is if the vertex of f(x)=-x^2+bx+8 has y-coordinate 17 and is in the second quadrant, find b. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75446 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=75446\">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%28x%29=-x%5E2%2Bbx%2B8 ALIGN=MIDDLE  ALT=\"f%28x%29=-x%5E2%2Bbx%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "To find the x-coordinate of the vertex, simply use this formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"x=-b%2F%282a%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=-b%2F%282%28-1%29%29 ALIGN=MIDDLE  ALT=\"x=-b%2F%282%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > So plug in a=-1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=b%2F2 ALIGN=MIDDLE  ALT=\"x=b%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "So the x value of the vertex is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=b%2F2 ALIGN=MIDDLE  ALT=\"x=b%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now plug this value in, as well as f(x)=17, to solve for b\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17=-%28b%2F2%29%5E2%2Bb%28b%2F2%29%2B8 ALIGN=MIDDLE  ALT=\"17=-%28b%2F2%29%5E2%2Bb%28b%2F2%29%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=b%2F2 ALIGN=MIDDLE  ALT=\"x=b%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and f(x)=17\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17=-b%5E2%2F4%2Bb%28b%2F2%29%2B8 ALIGN=MIDDLE  ALT=\"17=-b%5E2%2F4%2Bb%28b%2F2%29%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2F2 ALIGN=MIDDLE  ALT=\"b%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2F4 ALIGN=MIDDLE  ALT=\"b%5E2%2F4\"   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=17=-b%5E2%2F4%2Bb%5E2%2F2%2B8 ALIGN=MIDDLE  ALT=\"17=-b%5E2%2F4%2Bb%5E2%2F2%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=68=-b%5E2%2B2b%5E2%2B32 ALIGN=MIDDLE  ALT=\"68=-b%5E2%2B2b%5E2%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 4 to eliminate any fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-b%5E2%2B2b%5E2%2B32-68 ALIGN=MIDDLE  ALT=\"0=-b%5E2%2B2b%5E2%2B32-68\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 68 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=b%5E2-36 ALIGN=MIDDLE  ALT=\"0=b%5E2-36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%28b%2B6%29%28b-6%29 ALIGN=MIDDLE  ALT=\"0=%28b%2B6%29%28b-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the right side\r<BR>\n" );
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document.write( "Now set each factor equal to zero and solve\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B6=0 ALIGN=MIDDLE  ALT=\"b%2B6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b-6=0 ALIGN=MIDDLE  ALT=\"b-6=0\"   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=b=-6 ALIGN=MIDDLE  ALT=\"b=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <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;\" >\r<BR>\n" );
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document.write( "But since the vertex is in the second quadrant, the answer is \r<BR>\n" );
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document.write( "Notice if we plug in b=-6 into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-x%5E2%2Bbx%2B8 ALIGN=MIDDLE  ALT=\"f%28x%29=-x%5E2%2Bbx%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get\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%5E2-6x%2B8 ALIGN=MIDDLE  ALT=\"f%28x%29=-x%5E2-6x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and if we graph the equation we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-6%2C+5%2C+-2%2C+20%2C+-x%5E2-6x%2B8%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-6%2C+5%2C+-2%2C+20%2C+-x%5E2-6x%2B8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and we can see that the vertex has a y value at y=17 and it lies in the second quadrant. So our answer is verified. </SPAN>\n" );
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