document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126176>Question 126176</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)=3x2-18x+32 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92500 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=92500\">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%28-18%29%2F%282%2A3%29%29 ALIGN=MIDDLE  ALT=\"x=-%28%28-18%29%2F%282%2A3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  We are substituting -18 for b and 3 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%28-18%29%2F%286%29%29 ALIGN=MIDDLE  ALT=\"x=-%28%28-18%29%2F%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Simplification step 1  Multiplying 2 times 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%28%28-3%29%29 ALIGN=MIDDLE  ALT=\"x=-%28%28-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >           Simplification step 2  Dividing -18 by 6\r<BR>\n" );
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document.write( "<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;\" >              Simplification step 4  -1 times -3.<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.\r<BR>\n" );
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document.write( "2.  We now can substitute 3 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=%283%2A3%5E2-18%2A3%2B32%29 ALIGN=MIDDLE  ALT=\"y=%283%2A3%5E2-18%2A3%2B32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Each x in the original equation has been replaced <BR>\n" );
document.write( "                          with 3.\r<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=%283%2A3%5E2-18%2A3%2B32%29 ALIGN=MIDDLE  ALT=\"y=%283%2A3%5E2-18%2A3%2B32%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=%283%2A9-18%2A3%2B32%29 ALIGN=MIDDLE  ALT=\"y=%283%2A9-18%2A3%2B32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "B.  Simplify any multiplication    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2827-54%2B32%29 ALIGN=MIDDLE  ALT=\"y=%2827-54%2B32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "C.  Perform addition/subtraction   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2827-54%2B32%29 ALIGN=MIDDLE  ALT=\"y=%2827-54%2B32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   = 5\r<BR>\n" );
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document.write( "The Y coordinate of our axis of symmetry and vertex is 5.  \r<BR>\n" );
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document.write( "3. Therefore the vertex of the parabola is (3,5)  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+3%2Ax%5E2-18%2Ax%2B32%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C+200%2C+-6%2C+6%2C+-10%2C+10%2C+3%2Ax%5E2-18%2Ax%2B32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "                          \r<BR>\n" );
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document.write( " </SPAN>\n" );
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