document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126178>Question 126178</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to find the vertex of the parabola\r<BR>\n" );
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document.write( "f(x)=-x2+3x-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92508 by </B><A HREF=/tutors/aboutme.mpl?userid=JessicaGill><B>JessicaGill(40)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JessicaGill><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=92508\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To determine the vertex of a parabola without actually graphing it, you can use the following steps to obtain it.\r<BR>\n" );
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document.write( "1.  First use the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-+%28b%2F%282%2Aa%29%29 ALIGN=MIDDLE  ALT=\"x=-+%28b%2F%282%2Aa%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This represents the X coordinate of your axis of symmetry.  Note that your formula is in standard quadratic form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28a%2Ax%5E2%2Bb%2Ax%2Bc%29 ALIGN=MIDDLE  ALT=\"y=%28a%2Ax%5E2%2Bb%2Ax%2Bc%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Let's do the necessary substitutions and perform the necessary operations.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%28%283%29%2F%282%2A1%29%29 ALIGN=MIDDLE  ALT=\"x=-%28%283%29%2F%282%2A1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  We are substituting 3 for b and 1 for a.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%28%283%29%2F%282%29%29 ALIGN=MIDDLE  ALT=\"x=-%28%283%29%2F%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Simplification step 1  Multiplying 2 times 1 \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%28%283%29%2F2%29%29 ALIGN=MIDDLE  ALT=\"x=-%28%283%29%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >           Simplification step 2  Dividing 3 by 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;\" >              Simplification step 3  -1 times 3/2.<BR>\n" );
document.write( "                       The negative 1 (-1) comes from the negative of<BR>\n" );
document.write( "                       the entire formula.  See step 1 for the <BR>\n" );
document.write( "                       formula description.<BR>\n" );
document.write( "Our x coordinate for the vertex and axis of symmetry is -3/2 or -1 1/2.\r<BR>\n" );
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document.write( "2.  We now can substitute -3/2 into our original quadratic formula to solve for y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%28-3%2F2%29%5E2%2B3%2A%28-3%2F2%29-1%29 ALIGN=MIDDLE  ALT=\"y=%28%28-3%2F2%29%5E2%2B3%2A%28-3%2F2%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Each x in the original equation has been replaced with -3/2<BR>\n" );
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document.write( "Now to solve the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F2%29%5E2%2B3%2A%28-3%2F2%29-1%29 ALIGN=MIDDLE  ALT=\"y=%28-3%2F2%29%5E2%2B3%2A%28-3%2F2%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A.  Simplify the exponents    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=%289%2F4%29%2B3%2A%28-3%2F2%29-1 ALIGN=MIDDLE  ALT=\"Y=%289%2F4%29%2B3%2A%28-3%2F2%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >     <BR>\n" );
document.write( "        This involves multiplying fractions. <BR>\n" );
document.write( "        <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%2F2%29%2A%28-3%2F2%29=%289%2F4%29 ALIGN=MIDDLE  ALT=\"%28-3%2F2%29%2A%28-3%2F2%29=%289%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "B.  Simplify any multiplication   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=%289%2F4%29%2B3%2A%28-3%2F2%29-1 ALIGN=MIDDLE  ALT=\"Y=%289%2F4%29%2B3%2A%28-3%2F2%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >      <BR>\n" );
document.write( "        Again this involves multiplying whole  numbers and fractions.<BR>\n" );
document.write( "        <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F1%29%2A%28-3%2F2%29=%28-9%2F2%29 ALIGN=MIDDLE  ALT=\"%283%2F1%29%2A%28-3%2F2%29=%28-9%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "        <BR>\n" );
document.write( "C.  Perform addition/subtraction   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%289%2F4%29-%289%2F2%29-1%29 ALIGN=MIDDLE  ALT=\"y=%289%2F4%29-%289%2F2%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "        This  involves converting whole numbers to fractions and adding or <BR>\n" );
document.write( "        or subtracting, as the case may be.<BR>\n" );
document.write( "        <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2F4%29-%289%2F2%29-%281%2F1%29 ALIGN=MIDDLE  ALT=\"%289%2F4%29-%289%2F2%29-%281%2F1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2F4%29-%2818%2F4%29-%284%2F4%29 ALIGN=MIDDLE  ALT=\"%289%2F4%29-%2818%2F4%29-%284%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-15%2F4%29 ALIGN=MIDDLE  ALT=\"%28-15%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >OR<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3++3%2F4 ALIGN=MIDDLE  ALT=\"-3++3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The Y coordinate of our axis of symmetry and vertex is -3  3/4. <BR>\n" );
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document.write( "3. Therefore the vertex of the parabola is (-3/2,-3 3/4).<BR>\n" );
document.write( "If you would rather work in decimal form, convert each fraction to a decimal.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%2F2%29=-1.50 ALIGN=MIDDLE  ALT=\"%28-3%2F2%29=-1.50\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-15%2F4%29=-3.75 ALIGN=MIDDLE  ALT=\"%28-15%2F4%29=-3.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  See the graph below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C+200%2C+-6%2C+6%2C+-10%2C+10%2C+x%5E2%2B3%2Ax-1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C+200%2C+-6%2C+6%2C+-10%2C+10%2C+x%5E2%2B3%2Ax-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "                          <BR>\n" );
document.write( " </SPAN>\n" );
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