document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=58455>Question 58455</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here is a function that I have been dealing with at work:<BR>\n" );
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document.write( "Y(x) = –3.3x2 + 0.5x + 300.\r<BR>\n" );
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document.write( "I need to use this function to tell researchers what value of x produces the maximum output signal for an MRI machine, Y.  Also, since everyone’s MRI machine is not exactly the same as mine, I want to give them a range of x values that will produce nearly the maximum output Y.  So, here are the questions:<BR>\n" );
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document.write( "1.   What is the x value when Y is at its maximum value?\r<BR>\n" );
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document.write( "2.   What is the maximum value of Y?\r<BR>\n" );
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document.write( "3.   Since negative Y values are impossible for operating the MRI machine, what is the range of x values for Y to be greater than or equal to zero?\r<BR>\n" );
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document.write( "4.     What is the range of x values where Y is at 90% of its maximum value?\r<BR>\n" );
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document.write( "5.     Plot Graph showing all of the above information.\r<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 #40043 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=40043\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Y(x) = –3.3x2 + 0.5x + 300. <BR>\n" );
document.write( "I need to use this function to tell researchers what value of x produces the maximum output signal for an MRI machine, Y. Also, since everyone’s MRI machine is not exactly the same as mine, I want to give them a range of x values that will produce nearly the maximum output Y. So, here are the questions:\r<BR>\n" );
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document.write( "1. What is the x value when Y is at its maximum value? <BR>\n" );
document.write( "x=-b/2a = -0.5/-6.6=0.0757575...<BR>\n" );
document.write( "2. What is the maximum value of Y? 300.02<BR>\n" );
document.write( "3. Since negative Y values are impossible for operating the MRI machine, what is the range of x values for Y to be greater than or equal to zero?<BR>\n" );
document.write( "-9.459169<=x<=9.61068 <BR>\n" );
document.write( "4. What is the range of x values where Y is at 90% of its maximum value?<BR>\n" );
document.write( "0.9*300.02=279.018; -2.43424<=x<=2.5842 <BR>\n" );
document.write( "5. Plot Graph showing all of the above information. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28300%2C200%2C-12%2C12%2C-20%2C320%2C-3.3x%5E2%2B0.5x%2B300%29 ALIGN=MIDDLE  ALT=\"graph+%28300%2C200%2C-12%2C12%2C-20%2C320%2C-3.3x%5E2%2B0.5x%2B300%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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