document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=23687>Question 23687</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve the following quadratic equation. Any help or guidance you offer is greatly appreciated because I am very confused with these types of problems. \r<BR>\n" );
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document.write( "Find the vertex and intercepts for each quadratic function, and graph.\r<BR>\n" );
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document.write( "y = -x^2 + 2x + 3\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12430 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=12430\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the vertex:<BR>\n" );
document.write( "The x-coordinate of the vertex of a parabola is given by: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F2a ALIGN=MIDDLE  ALT=\"x+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Your quadratic equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x%5E2%2B2x%2B3 ALIGN=MIDDLE  ALT=\"y+=+-x%5E2%2B2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > where: a = -1, b = 2, and c = 3\r<BR>\n" );
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document.write( "The x-coordinate of the vertex is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2%2F2%28-1%29 ALIGN=MIDDLE  ALT=\"x+=+-2%2F2%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1 ALIGN=MIDDLE  ALT=\"x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The y-coordinate is found by substituting this value of x (1) into the quadratic equation and solving for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%281%29%5E2+%2B+2%281%29+%2B+3 ALIGN=MIDDLE  ALT=\"y+=+-%281%29%5E2+%2B+2%281%29+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-1+%2B+2+%2B+3 ALIGN=MIDDLE  ALT=\"y+=+-1+%2B+2+%2B+3\"   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 ALIGN=MIDDLE  ALT=\"y+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The vertex is at: (1, 4)\r<BR>\n" );
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document.write( "The (x) intercepts can be found by solving the quadratic equation for the two root (where the parabola crosses the x-axis, if the roots are real).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x%5E2+%2B+2x+%2B+3 ALIGN=MIDDLE  ALT=\"y+=+-x%5E2+%2B+2x+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set y = 0 because this is where the parabola will cross the x-axis.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2+%2B2x+%2B+3+=+0 ALIGN=MIDDLE  ALT=\"-x%5E2+%2B2x+%2B+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor -1 from the left side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x%5E2+-+2x+-+3%29+=+0 ALIGN=MIDDLE  ALT=\"-%28x%5E2+-+2x+-+3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the parentheses.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x+-+3%29%28x+%2B+1%29+=+0 ALIGN=MIDDLE  ALT=\"-%28x+-+3%29%28x+%2B+1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Clear the -1 by dividing both sides by -1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+3%29%28x+%2B+1%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+3%29%28x+%2B+1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the zero product principle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+3+=+0 ALIGN=MIDDLE  ALT=\"x+-+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and/or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+1+=+0 ALIGN=MIDDLE  ALT=\"x+%2B+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The roots (x-intercepts) are:<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "x = -1\r<BR>\n" );
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document.write( "Here's the graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-5%2C5%2C-5%2C6%2C-x%5E2%2B2x%2B3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-5%2C5%2C-5%2C6%2C-x%5E2%2B2x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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