document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1049701>Question 1049701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What must be the value of b so that the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2x%5E2+%2B+bx+%2B+4 ALIGN=MIDDLE  ALT=\"y+=+2x%5E2+%2B+bx+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a range of {y|y>=3} </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #665270 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=665270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Put into standard form using completing the square.  The equation in that form allows you to read the minimum value of the range directly in the standard form.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y=2%28x%2Bb%2F4%29%5E2%2B%2832-b%5E2%29%2F8%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y=2%28x%2Bb%2F4%29%5E2%2B%2832-b%5E2%29%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The parabola has a minimum value vertex, and the parabola opens upward.  You want range for y to be greater than or equal to 3, so set up the equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32-b%5E2=24 ALIGN=MIDDLE  ALT=\"32-b%5E2=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%5E2=24-32 ALIGN=MIDDLE  ALT=\"-b%5E2=24-32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=32-24=8 ALIGN=MIDDLE  ALT=\"b%5E2=32-24=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b=0%2B-+2%2Asqrt%282%29%29 ALIGN=MIDDLE  ALT=\"highlight%28b=0%2B-+2%2Asqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----------Either of these will work.  The vertical values are what you are interested in. </SPAN>\n" );
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