document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=716715>Question 716715</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Explain how you might go about constructing a quadratic equation whose solutions are -5 and 7.<BR>\n" );
document.write( "The connection between the graph and the equation is an important and helpful one! Briefly discuss the effect of the sign of the coefficient a on the graph of y = ax2 + bx + c. Please include two examples of graphs to support your thoughts, one where a < 0 and one where a > 0 \r<BR>\n" );
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document.write( "I have no idea how to explain or anything. Can someone help please? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #439945 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=439945\">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+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c++ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is the general equation for a parabola.<BR>\n" );
document.write( "It can either look like a cup that is holding<BR>\n" );
document.write( "water ( open up ), or a cup that is <BR>\n" );
document.write( "upside down ( open down )<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "The sign of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > tells which it is.<BR>\n" );
document.write( "To make it simple, suppose <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+0+ ALIGN=MIDDLE  ALT=\"+b+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+0+ ALIGN=MIDDLE  ALT=\"+c+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then you have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+ax%5E2+ ALIGN=MIDDLE  ALT=\"+y+=+ax%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Suppose <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+3+ ALIGN=MIDDLE  ALT=\"+a+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( cup holding water )<BR>\n" );
document.write( "Suppose <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-3+ ALIGN=MIDDLE  ALT=\"+a+=+-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( cup upside down )<BR>\n" );
document.write( "Here is a graph of both these cases:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+3x%5E2%2C+-3x%5E2+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+3x%5E2%2C+-3x%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------------------------<BR>\n" );
document.write( "The value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a ALIGN=MIDDLE  ALT=\"+a\"   DISABLED_style= \"max-width:90%; height:auto;\" > determines how fat or skinny <BR>\n" );
document.write( "the cup is. large <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, skinny cup, and<BR>\n" );
document.write( "small <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, fat cup<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "The numbers you pick for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+ ALIGN=MIDDLE  ALT=\"+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+ ALIGN=MIDDLE  ALT=\"+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "doesn't change these basic rules. They just move the<BR>\n" );
document.write( "graph around the x-y plane.<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "Suppose I compare:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+3x%5E2+%2B+4x+-+1+ ALIGN=MIDDLE  ALT=\"+y+=+3x%5E2+%2B+4x+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-3x%5E2+%2B+4x+-+1+ ALIGN=MIDDLE  ALT=\"+y+=+-3x%5E2+%2B+4x+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can see they just moved relative to where the vertexes<BR>\n" );
document.write( "were at the origin.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+3x%5E2+%2B+4x+-+1%2C+-3x%5E2+%2B+4x+-+1+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+3x%5E2+%2B+4x+-+1%2C+-3x%5E2+%2B+4x+-+1+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Hope this helps<BR>\n" );
document.write( " </SPAN>\n" );
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