document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=207794>Question 207794</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i posted these problems 4 days ago,but haven't received a response.could someone please help me.Thanks.\r<BR>\n" );
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document.write( "sketch the graphs,using the roots to find the function and the turning point\r<BR>\n" );
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document.write( "1.x = -8, x = 4<BR>\n" );
document.write( "2.x = -3, x = 3\r<BR>\n" );
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document.write( "thanks for the help.hagd<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 #157180 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=157180\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are given roots, so you can figure out the quadratic. I will do the first one, you can use the same process to do the second one<BR>\n" );
document.write( "1) roots are x=-8 and x=4<BR>\n" );
document.write( "You know that at the roots, the value of the function is 0<BR>\n" );
document.write( "You also know that for any product to equal zero, one or more terms in that function must be 0.<BR>\n" );
document.write( "Thus<BR>\n" );
document.write( "x =-8<BR>\n" );
document.write( "x+8 = 0<BR>\n" );
document.write( "x=<BR>\n" );
document.write( "4<BR>\n" );
document.write( "x-4=0<BR>\n" );
document.write( "Now you have the two terms for your equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B8%29%28x-4%29+=+f%28x%29 ALIGN=MIDDLE  ALT=\"%28x%2B8%29%28x-4%29+=+f%28x%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%5E2+-4x+%2B8x+-32+=+f%28x%29 ALIGN=MIDDLE  ALT=\"x%5E2+-4x+%2B8x+-32+=+f%28x%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%5E2+%2B+4x+-+32+=+f%28x%29 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4x+-+32+=+f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the equation for the first problem. Since is it q quadratic, you know it is a parabola that opens up (opens up since the x^2 term is positive). You also know that the 'turning point' will be halfway between the two root. Since the roots are 12 units apart, the 'turning point' will be 6 units from each root.<BR>\n" );
document.write( "-8+6 = -2<BR>\n" );
document.write( "4-6 = -2<BR>\n" );
document.write( "So find the value of f(x) when x=-2 and you'll have the minimum.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4x+-+32+=+f%28x%29 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4x+-+32+=+f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2+%2B4%2A2+-+32+=+f%282%29 ALIGN=MIDDLE  ALT=\"2%5E2+%2B4%2A2+-+32+=+f%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%2B+8+-+32+=+f%282%29 ALIGN=MIDDLE  ALT=\"4+%2B+8+-+32+=+f%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-20+=+f%282%29 ALIGN=MIDDLE  ALT=\"-20+=+f%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the 'turning point is the point (2,-20)<BR>\n" );
document.write( "Plot the funtion here --> http://www.wolframalpha.com/input/?i=x^2+%2B+4x+-+32+\r<BR>\n" );
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document.write( "Now do the same process for the other one. I am sure you can do it. If you still have questions, drop me an email <BR>\n" );
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