document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085653>Question 1085653</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Given the following polynomial: 2x^2 + 7x - 15 = 0   Check all that apply.\r<BR>\n" );
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document.write( "&#61600;	The value of the discriminant is 169.<BR>\n" );
document.write( "&#61600;	There are 2 real roots.<BR>\n" );
document.write( "&#61600;	There are 2 irrational roots.<BR>\n" );
document.write( "&#61600;	The graph intersects the y-axis twice.<BR>\n" );
document.write( "&#61600;	The parabola is directed upward.<BR>\n" );
document.write( "&#61600;	The axis of symmetry is located at: x = -7/4  <BR>\n" );
document.write( "&#61600;	The vertex is located at: (-7/4, -49/8)<BR>\n" );
document.write( "&#61600;	The roots are: {5,3/2}<BR>\n" );
document.write( "&#61600;	The graph intersects the y axis at (0, -15).<BR>\n" );
document.write( "&#61600;	The graph intersects the x-axis at (-5, 0) and (1.5, 0)\r<BR>\n" );
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document.write( "II.	<BR>\n" );
document.write( "Use the quadratic formula to solve the following: 3x^2 - x + 2 = 0     </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699713 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=699713\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "I. Given the following polynomial: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+7x+-+15+=+0+ ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+7x+-+15+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check all that apply.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=7%5E2-4%2A2%28-15%29=49%2B120=169 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=7%5E2-4%2A2%28-15%29=49%2B120=169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "&#61600; The value of the discriminant is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=169 ALIGN=MIDDLE  ALT=\"169\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "&#61600; There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+ ALIGN=MIDDLE  ALT=\"2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >real roots.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=discriminant%3E0 ALIGN=MIDDLE  ALT=\"discriminant%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so there are 2 real roots\r<BR>\n" );
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document.write( "&#61600; The parabola is directed upward.<BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is positive number, the  parabola<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+is ALIGN=MIDDLE  ALT=\"+is\"   DISABLED_style= \"max-width:90%; height:auto;\" > directed upward\r<BR>\n" );
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document.write( "&#61600; The axis of symmetry is located at: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-7%2F4 ALIGN=MIDDLE  ALT=\"x+=+-7%2F4\"   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=2+%28x+%2B+7%2F4%29%5E2+-+169%2F8+=+0 ALIGN=MIDDLE  ALT=\"2+%28x+%2B+7%2F4%29%5E2+-+169%2F8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-7%2F4 ALIGN=MIDDLE  ALT=\"h=-7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >->the axis of symmetry goes through vertex (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%2F4 ALIGN=MIDDLE  ALT=\"-7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+169%2F8 ALIGN=MIDDLE  ALT=\"-+169%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and it is a vertical line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-7%2F4 ALIGN=MIDDLE  ALT=\"x+=+-7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "&#61600; The graph intersects the y axis at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-15 ALIGN=MIDDLE  ALT=\"+-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E2+%2B+7x+-+15+ ALIGN=MIDDLE  ALT=\"y=2x%5E2+%2B+7x+-+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2A0%5E2+%2B+7x%2A+-+15 ALIGN=MIDDLE  ALT=\"y=2%2A0%5E2+%2B+7x%2A+-+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-15 ALIGN=MIDDLE  ALT=\"y=-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "&#61600; The graph intersects the x-axis at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)  and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5 ALIGN=MIDDLE  ALT=\"1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0 ALIGN=MIDDLE  ALT=\"+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+5%29+%282+x+-+3%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+5%29+%282+x+-+3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+5%29++=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+5%29++=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5 ALIGN=MIDDLE  ALT=\"x=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282+x+-+3%29+=+0+ ALIGN=MIDDLE  ALT=\"%282+x+-+3%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2=1.5+ ALIGN=MIDDLE  ALT=\"x=3%2F2=1.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5 ALIGN=MIDDLE  ALT=\"1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0 ALIGN=MIDDLE  ALT=\"+0\"   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=+graph%28+600%2C+600%2C+-10%2C+10%2C+-20%2C+10%2C+2x%5E2+%2B+7x+-+15%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-20%2C+10%2C+2x%5E2+%2B+7x+-+15%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "II.	<BR>\n" );
document.write( "Use the quadratic formula to solve the following: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+-+x+%2B+2+=+0+ ALIGN=MIDDLE  ALT=\"3x%5E2+-+x+%2B+2+=+0+\"   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=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%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=x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A3%2A2+%29%29%2F%282%2A3%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A3%2A2+%29%29%2F%282%2A3%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=x+=+%281+%2B-+sqrt%281-24+%29%29%2F6+ ALIGN=MIDDLE  ALT=\"x+=+%281+%2B-+sqrt%281-24+%29%29%2F6+\"   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=x+=+%281+%2B-+sqrt%28-23+%29%29%2F6+ ALIGN=MIDDLE  ALT=\"x+=+%281+%2B-+sqrt%28-23+%29%29%2F6+\"   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=x+=+%281+%2B-+i%2Asqrt%2823+%29%29%2F6+ ALIGN=MIDDLE  ALT=\"x+=+%281+%2B-+i%2Asqrt%2823+%29%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281%2F6%29%281+-+i%2Asqrt%2823+%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%281%2F6%29%281+-+i%2Asqrt%2823+%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( " </SPAN>\n" );
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