document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=35924>Question 35924</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the quadratic function   y  =  x 2  - 4 x  +  3  , respond to the following:\r<BR>\n" );
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document.write( "a)	Does the graph open up or down?\r<BR>\n" );
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document.write( "b)  What is the equation of the axis of symmetry? <BR>\n" );
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document.write( "c)  What are the coordinates of the vertex?\r<BR>\n" );
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document.write( "            d)   Give the y intercept.\r<BR>\n" );
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document.write( "e)   Give the x intercept(s).\r<BR>\n" );
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document.write( "	f)     Sketch the graph<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #22000 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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/cgi-bin/show-face.mpl?user=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=22000\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y++=++x%5E+2++-+4+x++%2B++3 ALIGN=MIDDLE  ALT=\"y++=++x%5E+2++-+4+x++%2B++3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is a parabola that opens up, since the coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is positive.  \r<BR>\n" );
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document.write( "You can complete the square or use a formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"x+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the vertex and the line of symmetry.  \r<BR>\n" );
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document.write( "Completing the square looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y++=++x%5E+2++-+4+x++%2B++3 ALIGN=MIDDLE  ALT=\"y++=++x%5E+2++-+4+x++%2B++3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take half of the x coefficient (which is -2) and square it (which is 4), and add and subtract 4 from the right side of the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y++=++x%5E+2++-+4+x++%2B+_____%2B++3+-+_____ ALIGN=MIDDLE  ALT=\"y++=++x%5E+2++-+4+x++%2B+_____%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++=++x%5E+2++-+4+x++%2B+4%2B++3+-+4 ALIGN=MIDDLE  ALT=\"y++=++x%5E+2++-+4+x++%2B+4%2B++3+-+4\"   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=y+=+%28x-2%29%5E2+-1 ALIGN=MIDDLE  ALT=\"y+=+%28x-2%29%5E2+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The line of symmetry will be the value of x that \"zeros out the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%29+ ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which will be x=2.  This will also be the x coordinate of the vertex.  To find the y coordinate of the vertex, let x= 2, and you have y = -1.\r<BR>\n" );
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document.write( "Vertex = (2,-1)\r<BR>\n" );
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document.write( "The y intercept is where x = 0.  If x = 0, then y =3.\r<BR>\n" );
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document.write( "The x intercept is where y = 0.  If y = 0, then <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+x%5E2+-+4x%2B3 ALIGN=MIDDLE  ALT=\"0=+x%5E2+-+4x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+%28x-3%29%28x-1%29 ALIGN=MIDDLE  ALT=\"0+=+%28x-3%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the x intercepts will be at x =3 and x= 1.\r<BR>\n" );
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document.write( "Graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C+-4%2C+8%2C+-4%2C10%2C+x%5E2+-4x%2B3%29+ ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C+-4%2C+8%2C+-4%2C10%2C+x%5E2+-4x%2B3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "R^2 at SCC\r<BR>\n" );
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