document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=472224>Question 472224</A>: <I><SPAN STYLE=\"word-break: break-all;\"> -3 is less than or equal to a, and a is less than or equal to 1.<BR>\n" );
document.write( "b = 4 - a^2\r<BR>\n" );
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document.write( "Using the facts above, what number is obtained when the smallest possible value of b is subtracted from the largest possible value of b?\r<BR>\n" );
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document.write( "Please explain, I do not understand. Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #323792 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=323792\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since a^2 is always nonnegative, for large-magnitude values of a, 4 - a^2 will decrease the value of b. To find the maximum value for b, we find the minimal value of a^2, which occurs when a = 0. This implies the maximum value of b is 4.\r<BR>\n" );
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document.write( "To minimize b, we maximize a^2 by setting a = -3 (the number contained in the domain with the highest absolute value). The least possible value of b is 4 - (-3)^2 = -5.\r<BR>\n" );
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document.write( "Hence the difference between the two is 4 - (-5) = 9. </SPAN>\n" );
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