document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=91110>Question 91110</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find y-intercept and vertex y = x^2 - 3x - 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #66134 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=66134\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the y-intercept, plug in x=0\r<BR>\n" );
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document.write( "Lets find the value of y when  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=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=y=x%5E2-3x-4 ALIGN=MIDDLE  ALT=\"y=x%5E2-3x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given polynomial\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%280%29%5E2-3%280%29-4 ALIGN=MIDDLE  ALT=\"y=%280%29%5E2-3%280%29-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=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=y=%280%29-3%280%29-4 ALIGN=MIDDLE  ALT=\"y=%280%29-3%280%29-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise 0 to the second power to get 0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%280%29-0-4 ALIGN=MIDDLE  ALT=\"y=%280%29-0-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 3 by 0 to get 0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4 ALIGN=MIDDLE  ALT=\"y=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Remove any zero terms\r<BR>\n" );
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document.write( "So when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4 ALIGN=MIDDLE  ALT=\"y=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the y-intercept is (0,-4)\r<BR>\n" );
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document.write( "To determine the x-value of the vertex, 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( "From the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-3x-4 ALIGN=MIDDLE  ALT=\"y=x%5E2-3x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that a=1 and b=-3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28--3%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x=%28--3%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in b=-3 and a=1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x=3%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -3 to get 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%283%29%2F2 ALIGN=MIDDLE  ALT=\"x=%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 1 to get 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the x-coordinate of the vertex is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.5 ALIGN=MIDDLE  ALT=\"x=1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > in decimal form). Lets plug this into the equation to find the y-coordinate of the vertex.\r<BR>\n" );
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document.write( "Lets evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281.5%29 ALIGN=MIDDLE  ALT=\"f%281.5%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=f%28x%29=x%5E2-3x-4 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2-3x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given polynomial\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281.5%29=%281.5%29%5E2-3%281.5%29-4 ALIGN=MIDDLE  ALT=\"f%281.5%29=%281.5%29%5E2-3%281.5%29-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.5 ALIGN=MIDDLE  ALT=\"x=1.5\"   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%281.5%29=2.25-3%281.5%29-4 ALIGN=MIDDLE  ALT=\"f%281.5%29=2.25-3%281.5%29-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise 1.5 to the second power to get 2.25\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281.5%29=2.25-4.5-4 ALIGN=MIDDLE  ALT=\"f%281.5%29=2.25-4.5-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -3 and 1.5 to get -4.5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281.5%29=-6.25 ALIGN=MIDDLE  ALT=\"f%281.5%29=-6.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "So the vertex is (1.5,-6.25)\r<BR>\n" );
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document.write( "Here is a graph to see the vertex and y-intercept \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+-10%2C+10%2C+-10%2C+10%2C+x%5E2-3x-4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-3x-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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