document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196808>Question 1196808</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sketch the following functions by first solving for the x intercepts using the quadratic formula.  If there are no x intercepts then use the method explained in class...this makes use of the fact that raising or lowering a parabola by some amount does not change the x coordinate of the vertex.  So...remove the constant from the right side, factor what's left to determine x intercepts.  The average of those is the x coordinate of the vertex.  Then substitute that back into the original equation to solve for the y coordinate of the vertex. <BR>\n" );
document.write( "y = 3x^2+15x+30   AND   y = -x^2+4x-8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829811 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=829811\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is not the full solution.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%5E2%2B5x%2B10%2B%285%2F2%29%5E2-%285%2F2%29%5E2%29 ALIGN=MIDDLE  ALT=\"3%28x%5E2%2B5x%2B10%2B%285%2F2%29%5E2-%285%2F2%29%5E2%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=3%28x%5E2%2B5x%2B%285%2F2%29%5E2%2B10-%285%2F2%29%5E2%29 ALIGN=MIDDLE  ALT=\"3%28x%5E2%2B5x%2B%285%2F2%29%5E2%2B10-%285%2F2%29%5E2%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=3%28%28x%2B5%2F2%29%5E2%2B40%2F4-25%2F4%29 ALIGN=MIDDLE  ALT=\"3%28%28x%2B5%2F2%29%5E2%2B40%2F4-25%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28%28x%2B5%2F2%29%5E2%2B15%2F4%29 ALIGN=MIDDLE  ALT=\"3%28%28x%2B5%2F2%29%5E2%2B15%2F4%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=3%28x%2B5%2F2%29%5E2%2B45%2F4 ALIGN=MIDDLE  ALT=\"3%28x%2B5%2F2%29%5E2%2B45%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%28x%2B5%2F2%29%5E2%2B11%261%2F4 ALIGN=MIDDLE  ALT=\"y=3%28x%2B5%2F2%29%5E2%2B11%261%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----------you can read the vertex and solve for the roots.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x%5E2-4x%2B8%29 ALIGN=MIDDLE  ALT=\"-%28x%5E2-4x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x%5E2-4x%2B4-4%2B8%29 ALIGN=MIDDLE  ALT=\"-%28x%5E2-4x%2B4-4%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28%28x-2%29%5E2%2B4%29 ALIGN=MIDDLE  ALT=\"-%28%28x-2%29%5E2%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%28x-2%29%5E2-4 ALIGN=MIDDLE  ALT=\"y=-%28x-2%29%5E2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >--------------you can read the vertex and solve for the roots. </SPAN>\n" );
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