document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=18332>Question 18332</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi all,\r<BR>\n" );
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document.write( "I am having a meltdown with Quadratic equations, vertexes and intercepts. Could someone please help me uunderstand this problem?\r<BR>\n" );
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document.write( "Find the vertex and intercepts for the quadratic function , and sketch its graph:<BR>\n" );
document.write( "y = x^2 - 4x -12\r<BR>\n" );
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document.write( "Thank you very much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #8782 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=8782\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Once your quadratic equation is in the standard form:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c%5D=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c%5D=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the x-coordinate of the vertex is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F2a ALIGN=MIDDLE  ALT=\"-b%2F2a\"   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%2F2a+=+-%28-4%29%2F2%281%29 ALIGN=MIDDLE  ALT=\"-b%2F2a+=+-%28-4%29%2F2%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F2+=+2 ALIGN=MIDDLE  ALT=\"4%2F2+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now find the y-coordinate of the vertex by substituting this value of x (x=2) into the quadratic equation and 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+=+%282%29%5E2+-+4%282%29+-+2 ALIGN=MIDDLE  ALT=\"y+=+%282%29%5E2+-+4%282%29+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4+-+8+-+12 ALIGN=MIDDLE  ALT=\"y+=+4+-+8+-+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-16 ALIGN=MIDDLE  ALT=\"y+=+-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The vertex is at (2, -16)\r<BR>\n" );
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document.write( "The x-intercepts can be found by solving the quadratic equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+4x+-+12+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+4x+-+12+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve by factoring.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%28x-6%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%28x-6%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the zero products principle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2+=+0 ALIGN=MIDDLE  ALT=\"x%2B2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and/or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-6+=+0 ALIGN=MIDDLE  ALT=\"x-6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If x+2 = 0, then x = -2<BR>\n" );
document.write( "If x-6 = 0, then x = 6<BR>\n" );
document.write( "The x-intercepts are: (-2, 0) and (6, 0)\r<BR>\n" );
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document.write( "See the graph below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-20%2C10%2Cx%5E2-4x-12%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-20%2C10%2Cx%5E2-4x-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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