document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=258558>Question 258558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
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document.write( "This is what my book says for the four problems I need help on:\r<BR>\n" );
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document.write( "For each of the following functions, reason with the symbolic forms to find all x for which f(x)=0. Then sketch a graph and find the minimum or maximum value of the function.<BR>\n" );
document.write( "1. d(x)=(2x-5)(x+4)<BR>\n" );
document.write( "2. f(x)=x^2+5x-6<BR>\n" );
document.write( "3. g(x)=x^2-12x<BR>\n" );
document.write( "4. h(x)=-x^2+7x+18\r<BR>\n" );
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document.write( "I think I would be fine sketching the graph. But I'm just not too sure on how to get to that point.\r<BR>\n" );
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document.write( "Thank you very much for your help.\r<BR>\n" );
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document.write( "K. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #190377 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=190377\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets take each one separately:<BR>\n" );
document.write( "1. d(x)=(2x-5)(x+4)<BR>\n" );
document.write( "set d(x) = 0 to get<BR>\n" );
document.write( "(2x-5)(x+4) = 0<BR>\n" );
document.write( "set each parenthesis = 0 and solve for x to get<BR>\n" );
document.write( "(2x-5)=0<BR>\n" );
document.write( "2x=5<BR>\n" );
document.write( "x = 5/2<BR>\n" );
document.write( "and then<BR>\n" );
document.write( "x+4=0<BR>\n" );
document.write( "x=-4<BR>\n" );
document.write( "The minimum occurs at (-3/4, -21.125)<BR>\n" );
document.write( "graph is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+10%2C+-30%2C+10%2C+%282x-5%29%28x%2B4%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+10%2C+-30%2C+10%2C+%282x-5%29%28x%2B4%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "2. f(x)=x^2+5x-6<BR>\n" );
document.write( "factoring, we get<BR>\n" );
document.write( "(x+6)(x-1)<BR>\n" );
document.write( "Set f(x) = 0 to get<BR>\n" );
document.write( "(x+6)(x-1) = 0<BR>\n" );
document.write( "Set each parenthesis = 0 and solve for x to get<BR>\n" );
document.write( "(x+6)=0<BR>\n" );
document.write( "x = -6<BR>\n" );
document.write( "and then<BR>\n" );
document.write( "x-1=0<BR>\n" );
document.write( "x=1<BR>\n" );
document.write( "The minimum occurs at (-5/2, 12.75)<BR>\n" );
document.write( "graph is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+10%2C+-20%2C+20%2C+x%5E2%2B5x-6%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+10%2C+-20%2C+20%2C+x%5E2%2B5x-6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "3. g(x)=x^2-12x<BR>\n" );
document.write( "factoring, we get<BR>\n" );
document.write( "(x)(x-12)<BR>\n" );
document.write( "Set f(x) = 0 to get<BR>\n" );
document.write( "(x)(x-12) = 0<BR>\n" );
document.write( "Set each parenthesis = 0 and solve for x to get<BR>\n" );
document.write( "x=0<BR>\n" );
document.write( "and then<BR>\n" );
document.write( "x-12=0<BR>\n" );
document.write( "x=12<BR>\n" );
document.write( "The minimum occurs at (6, -36)<BR>\n" );
document.write( "graph is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+10%2C+-40%2C+20%2C+x%5E2-12x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+10%2C+-40%2C+20%2C+x%5E2-12x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "4. h(x)=-x^2+7x+18 <BR>\n" );
document.write( "factoring, we get<BR>\n" );
document.write( "-1(x+2)(x-9)<BR>\n" );
document.write( "Set f(x) = 0 to get<BR>\n" );
document.write( "(x+2)(x-9) = 0<BR>\n" );
document.write( "Set each parenthesis = 0 and solve for x to get<BR>\n" );
document.write( "x+2=0<BR>\n" );
document.write( "x = -2<BR>\n" );
document.write( "and then<BR>\n" );
document.write( "x-9=0<BR>\n" );
document.write( "x=9<BR>\n" );
document.write( "The maximum occurs at (7/2, 30.25)<BR>\n" );
document.write( "graph is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+10%2C+-20%2C+40%2C+-x%5E2%2B7x%2B18%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+10%2C+-20%2C+40%2C+-x%5E2%2B7x%2B18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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