document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=308022>Question 308022</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the maximum or minimum value of the quardratic function ?\r<BR>\n" );
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document.write( "f(x)=3x^2+12x+8\r<BR>\n" );
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document.write( "a. -28\r<BR>\n" );
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document.write( "b. -4\r<BR>\n" );
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document.write( "c. -2\r<BR>\n" );
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document.write( "d. 44\r<BR>\n" );
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document.write( "tthanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #220263 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=220263\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can either differentiate and find when the derivative is zero. <BR>\n" );
document.write( "f(x)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B12x%2B8+ ALIGN=MIDDLE  ALT=\"3x%5E2%2B12x%2B8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "f'(x)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B12=0+ ALIGN=MIDDLE  ALT=\"6x%2B12=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2+ ALIGN=MIDDLE  ALT=\"x=-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29=3%284%29%2B12%28-2%29%2B8+ ALIGN=MIDDLE  ALT=\"f%28-2%29=3%284%29%2B12%28-2%29%2B8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29=12-24%2B8=-4+ ALIGN=MIDDLE  ALT=\"f%28-2%29=12-24%2B8=-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the second derivative to find whether its min or max.<BR>\n" );
document.write( "f''(x)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%3E0+ ALIGN=MIDDLE  ALT=\"6%3E0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the second derivative is positive, the value is a minimum.<BR>\n" );
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document.write( "Or algebraically complete the square to find the vertex form,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=3x%5E2%2B12x%2B8+ ALIGN=MIDDLE  ALT=\"f%28x%29=3x%5E2%2B12x%2B8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=3%28x%5E2%2B4x%29%2B8+ ALIGN=MIDDLE  ALT=\"f%28x%29=3%28x%5E2%2B4x%29%2B8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=3%28x%5E2%2B4x%2B4%29%2B8-12+ ALIGN=MIDDLE  ALT=\"f%28x%29=3%28x%5E2%2B4x%2B4%29%2B8-12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29=3%28x%2B2%29%5E2-4+ ALIGN=MIDDLE  ALT=\"+f%28x%29=3%28x%2B2%29%5E2-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the <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;\" > coefficient is positive (3), the parabola opens upwards and the value at the vertex is a minimum and occurs at (-2,-4). <BR>\n" );
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document.write( "b) is the correct answer.<BR>\n" );
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